quadratic equations and applications objective: to use different methods to solve quadratic...
TRANSCRIPT
![Page 1: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/1.jpg)
Quadratic Equations and Applications
Objective: To use different methods to solve quadratic
equations.
![Page 2: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/2.jpg)
Factoring
• Factoring is an effective way to solve quadratic equations.
![Page 3: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/3.jpg)
Factoring
• Solve the following: 02452 xx
![Page 4: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/4.jpg)
Factoring
• Solve the following:
• This is the easiest type because you always start this way.
02452 xx
__)__)(( xx
![Page 5: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/5.jpg)
Factoring
• Solve the following:
• This is the easiest type because you always start this way. Since the last term is negative, the signs must be opposite.
02452 xx
_)_)(( xx
![Page 6: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/6.jpg)
Factoring
• Solve the following:
• Since the middle term is – 5x, that means that the outer and inner terms are different by 5, and the larger term is negative.
02452 xx
_)_)(( xx
![Page 7: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/7.jpg)
Factoring
• Solve the following:
• Since the middle term is – 5x, that means that the outer and inner terms are different by 5, and the larger term is negative.
• We now need factors of 24 that are different by 5.
02452 xx
_)_)(( xx
![Page 8: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/8.jpg)
Factoring
• Solve the following:
• Since the middle term is – 5x, that means that the outer and inner terms are different by 5, and the larger term is negative.
• We now need factors of 24 that are different by 5.
02452 xx
0)8)(3( xx
![Page 9: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/9.jpg)
Factoring
• Solve the following:
• We know that if two things multiplied together equal zero, one of them must be zero.
or
02452 xx
0)8)(3( xx
3
03
x
x8
08
x
x
![Page 10: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/10.jpg)
Factoring
• Solve the following: 024102 xx
![Page 11: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/11.jpg)
Factoring
• Solve the following:
• Since the last term is positive, both factors are the same sign, and since the middle term is positive, they are both positive.
024102 xx
_)_)(( xx
![Page 12: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/12.jpg)
Factoring
• Solve the following:
• Since the last term is positive, both factors are the same sign, and since the middle term is positive, they are both positive.
• We need factors of 24 that add to get 10.
024102 xx
_)_)(( xx
![Page 13: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/13.jpg)
Factoring
• Solve the following:
• Since the last term is positive, both factors are the same sign, and since the middle term is positive, they are both positive.
• We need factors of 24 that add to get 10.
024102 xx
0)4)(6( xx
![Page 14: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/14.jpg)
Factoring
• Solve the following:
• Solve:
or
024102 xx
0)4)(6( xx
6
06
x
x
4
04
x
x
![Page 15: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/15.jpg)
You Try
• Solve the following: 036132 xx
![Page 16: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/16.jpg)
You Try
• Solve the following:
• Since the last term is positive, both factors are the same sign, and now since the middle term is negative, they are both negative.
• We need factors of 36 that add to get 13.
036132 xx
0)4)(9( xx
9
09
x
x
4
04
x
x
![Page 17: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/17.jpg)
Factoring
• Solve: 3792 2 xx
![Page 18: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/18.jpg)
Factoring
• Solve:
• First, set the equation equal to zero.
3792 2 xx
0492 2 xx
![Page 19: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/19.jpg)
Factoring
• Solve:
• First, set the equation equal to zero.
• This is how we start:
3792 2 xx
0492 2 xx
_)_)(2( xx
![Page 20: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/20.jpg)
Factoring
• Solve:
• First, set the equation equal to zero.
• This is how we start:• We need factors of 4 that will make the outer and
inner terms add to get 9.
3792 2 xx
0492 2 xx
_)_)(2( xx
![Page 21: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/21.jpg)
Factoring
• Solve:
• First, set the equation equal to zero.
• This is how we start:• We need factors of 4 that will make the outer and
inner terms add to get 9.
3792 2 xx
0492 2 xx
_)_)(2( xx
0)4)(12( xx 2/1
012
x
x
4
04
x
x
![Page 22: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/22.jpg)
Factoring
• Solve: 036 2 xx
![Page 23: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/23.jpg)
Factoring
• Solve:
• With only two terms, we look for a greatest common factor.
or
036 2 xx
0)12(3 xx
0
03
x
x
21
012
x
x
![Page 24: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/24.jpg)
Square Roots
• Solve: 124 2 x
![Page 25: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/25.jpg)
Square Roots
• Solve:
• First, isolate the variable and get the x2 alone.
124 2 x
32 x
![Page 26: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/26.jpg)
Square Roots
• Solve:
• First, isolate the variable and get the x2 alone.
• Square root both sides.
124 2 x
32 x
3x
![Page 27: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/27.jpg)
Square Roots
• Solve: 7)3( 2 x
![Page 28: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/28.jpg)
Square Roots
• Solve:
• The x is by itself as much as it can be, so square root both sides.
7)3( 2 x
73 x
![Page 29: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/29.jpg)
Square Roots
• Solve:
• The x is by itself as much as it can be, so square root both sides.
• Add 3 to both sides to solve for x.
7)3( 2 x
73 x
73x
![Page 30: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/30.jpg)
Square Roots
• You Try: 16)6( 2 x
![Page 31: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/31.jpg)
Square Roots
• You Try: 16)6( 2 x
46 x
1046
246
46
x
![Page 32: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/32.jpg)
Class Work
• Page 120
• 8-14 even
• 22, 24, 26, 28
![Page 33: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/33.jpg)
Homework
• Page 120
• 7-15 odd
• 21-31 odd
![Page 34: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/34.jpg)
Completing the Square
• When completing the square, we follow the same technique each time.
![Page 35: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/35.jpg)
Completing the Square
• When completing the square, we follow the same technique each time.
1. Variables on one side, constants on the other.
![Page 36: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/36.jpg)
Completing the Square
• When completing the square, we follow the same technique each time.
1. Variables on one side, constants on the other.2. Make sure the x2 is a 1x2.
![Page 37: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/37.jpg)
Completing the Square
• When completing the square, we follow the same technique each time.
1. Variables on one side, constants on the other.2. Make sure the x2 is a 1x2.3. Take half of the middle term and square it.
![Page 38: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/38.jpg)
Completing the Square
• When completing the square, we follow the same technique each time.
1. Variables on one side, constants on the other.2. Make sure the x2 is a 1x2.3. Take half of the middle term and square it.4. Add that number to both sides.
![Page 39: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/39.jpg)
Completing the Square
• When completing the square, we follow the same technique each time.
1. Variables on one side, constants on the other.2. Make sure the x2 is a 1x2.3. Take half of the middle term and square it.4. Add that number to both sides.5. Solve.
![Page 40: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/40.jpg)
Completing the Square
• Solve: 0822 xx
![Page 41: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/41.jpg)
Completing the Square
• Solve:
• Add eight to both sides.
0822 xx
822 xx
![Page 42: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/42.jpg)
Completing the Square
• Solve:
• Add eight to both sides.• Take half of 2, square it, and add it to both sides.
0822 xx
18122 xx
822 xx
![Page 43: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/43.jpg)
Completing the Square
• Solve:
• Add eight to both sides.• Take half of 2, square it, and add it to both sides.
• Solve.
0822 xx
9)1( 2 x
822 xx
18122 xx
31 x
![Page 44: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/44.jpg)
Completing the Square
• Solve:
• Add eight to both sides.• Take half of 2, square it, and add it to both sides.
• Solve.
0822 xx
9)1( 2 x
822 xx
18122 xx
31 x
2
31
x
x
4
31
x
x
![Page 45: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/45.jpg)
Completing the Square
• You Try:0382 xx
![Page 46: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/46.jpg)
Completing the Square
• Solve:0382 xx
382 xx
![Page 47: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/47.jpg)
Completing the Square
• Solve:0382 xx
382 xx
163)4(8 22 xx
![Page 48: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/48.jpg)
Completing the Square
• Solve:0382 xx
382 xx
1631682 xx
13)4( 2 x
134 x 134x
![Page 49: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/49.jpg)
Completing the Square
• You Try:01642 xx
![Page 50: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/50.jpg)
Completing the Square
• Solve:01642 xx
1642 xx
416442 xx
20)2( 2 x
![Page 51: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/51.jpg)
Completing the Square
• Solve:01642 xx
1642 xx
416442 xx
20)2( 2 x
202 x 522x
![Page 52: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/52.jpg)
Completing the Square
• Solve: 0382 2 xx
382 2 xx
2/342 xx
![Page 53: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/53.jpg)
Completing the Square
• Solve: 0382 2 xx
382 2 xx
2/342 xx
42/3442 xx
2/5)2( 2 x
![Page 54: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/54.jpg)
Completing the Square
• Solve: 0382 2 xx
382 2 xx
2/342 xx
42/3442 xx
2/5)2( 2 x
2/52 x
![Page 55: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/55.jpg)
Completing the Square
• Solve: 0382 2 xx
382 2 xx
2/342 xx
42/3442 xx
2/5)2( 2 x
2/52 x
2/52x
![Page 56: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/56.jpg)
Completing the Square
• Solve: 0382 2 xx
382 2 xx
2/342 xx
42/3442 xx
2/5)2( 2 x
2/52 x
2/52x
2
102x
![Page 57: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/57.jpg)
Rationalize
• Rationalize the following:2
5
![Page 58: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/58.jpg)
Rationalize
• Rationalize the following:2
5
2
5
![Page 59: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/59.jpg)
Rationalize
• Rationalize the following:2
5
2
2
2
5
![Page 60: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/60.jpg)
Rationalize
• Rationalize the following:2
5
2
10
2
2
2
5
![Page 61: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/61.jpg)
Rationalize
• You Try.
7
3
11
5
![Page 62: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/62.jpg)
Rationalize
• You Try.
7
3
11
5
7
21
7
7
7
3
11
55
11
11
11
5
![Page 63: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/63.jpg)
The Quadratic Formula
• Given a quadratic equation of the form:
• We can solve it using the quadratic formula:
0,02 acbxax
a
acbb
2
42
![Page 64: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/64.jpg)
The Quadratic Formula
• Solve using the quadratic formula. 932 xx
![Page 65: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/65.jpg)
The Quadratic Formula
• Solve using the quadratic formula.• Set the equation equal to zero.
932 xx
0932 xx
![Page 66: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/66.jpg)
The Quadratic Formula
• Solve using the quadratic formula.• Set the equation equal to zero.• a=1, b=3, c=-9
932 xx
0932 xx
![Page 67: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/67.jpg)
The Quadratic Formula
• Solve using the quadratic formula.• Set the equation equal to zero.• a=1, b=3, c=-9• Use the quadratic equation.
932 xx
0932 xx
)1(2)9)(1(4)3(3 2
![Page 68: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/68.jpg)
The Quadratic Formula
• Solve using the quadratic formula.• Set the equation equal to zero.• a=1, b=3, c=-9• Use the quadratic equation.
932 xx
0932 xx
2
3693)1(2
)9)(1(4)3(3 2
![Page 69: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/69.jpg)
The Quadratic Formula
• Solve using the quadratic formula.• Set the equation equal to zero.• a=1, b=3, c=-9• Use the quadratic equation.
932 xx
0932 xx
2
3693)1(2
)9)(1(4)3(3 2
2
533
2
453
![Page 70: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/70.jpg)
The Quadratic Formula
• Solve using the quadratic formula. 462 xx
![Page 71: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/71.jpg)
The Quadratic Formula
• Solve using the quadratic formula.• Set the equation equal to zero.• a=1, b=-6, c=-4
462 xx
0462 xx
![Page 72: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/72.jpg)
The Quadratic Formula
• Solve using the quadratic formula.• Set the equation equal to zero.• a=1, b=-6, c=-4• Use the quadratic equation.
462 xx
0462 xx
2
16366)1(2
)4)(1(4)6(6 2
1332
1326
2
526
![Page 73: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/73.jpg)
Class Work
• Page 120
• 35, 37, 38
![Page 74: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/74.jpg)
Class Work
• Page 120
• 35, 37, 38
• 68, 72, 74, 76
![Page 75: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/75.jpg)
Example 7
• A bedroom is 3 feet longer than it is wide and has an area of 154 square feet. Find the dimensions of the room.
![Page 76: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/76.jpg)
Example 7
• A bedroom is 3 feet longer than it is wide and has an area of 154 square feet. Find the dimensions of the room.
• The width will be x• The length will be x + 3
![Page 77: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/77.jpg)
Example 7
• A bedroom is 3 feet longer than it is wide and has an area of 154 square feet. Find the dimensions of the room.
• The width will be x• The length will be x + 3• Since the area is length x width, the equation is:
x(x+3) = 154
![Page 78: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/78.jpg)
Ex. 7
• We need to solve the equation to find x.
154)3( xx
015432 xx
![Page 79: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/79.jpg)
Ex. 7
• We need to solve the equation to find x.
154)3( xx
015432 xx
0)14)(11( xx
11,011 xx 14,014 xx
![Page 80: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/80.jpg)
Ex. 7
• Since x is the width of a room, it can’t be negative. The only answer we will use is x = 11.
• This means the width is 11 and the length is 14.
![Page 81: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/81.jpg)
Example 9
• From 2000 to 2007, the estimated number of Internet users I (in millions) in the United States can be modeled by the quadratic equation
• where t represents the year, with t = 0 being 2000. In what year will the number of Internet users surpass 180 million?
,9.12519.17163.1 2 ttI 70 t
![Page 82: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/82.jpg)
Ex. 9
• We will use our calculator to solve the following problem.
1809.12519.17163.1 2 tt
![Page 83: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/83.jpg)
Ex. 9
• We will use our calculator to solve the following problem.
1809.12519.17163.1 2 tt
01.5419.17163.1 2 tt
![Page 84: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/84.jpg)
Ex. 9
• We will use our calculator to solve the following problem.
1809.12519.17163.1 2 tt
01.5419.17163.1 2 tt
2.105.4 ort
2004
![Page 85: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/85.jpg)
Example 10
• An L-shaped sidewalk from the athletic center to the library on a college campus is shown. The length of one sidewalk forming the L is twice as long as the other. The length of the diagonal between the two buildings is 32 feet. How many feet does a person save by walking on the diagonal?
![Page 86: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/86.jpg)
Example 10
• An L-shaped sidewalk from the athletic center to the library on a college campus is shown. The length of one sidewalk forming the L is twice as long as the other. The length of the diagonal between the two buildings is 32 feet. How many feet does a person save by walking on the diagonal?
• Let x = one path• Let 2x = the other path
![Page 87: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/87.jpg)
Example 10
• An L-shaped sidewalk from the athletic center to the library on a college campus is shown. The length of one sidewalk forming the L is twice as long as the other. The length of the diagonal between the two buildings is 32 feet. How many feet does a person save by walking on the diagonal?
• Let x = one path• Let 2x = the other path• We will use the Pythagorean Theorem to solve.
![Page 88: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/88.jpg)
Ex. 10
222 32)2( xx
![Page 89: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/89.jpg)
Ex. 10
222 32)2( xx
10245 2 x
![Page 90: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/90.jpg)
Ex. 10
222 32)2( xx
10245 2 x
8.2042 x
![Page 91: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/91.jpg)
Ex. 10
222 32)2( xx
10245 2 x
8.2042 x
8.204x
![Page 92: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/92.jpg)
Ex. 10
222 32)2( xx
10245 2 x
8.2042 x
8.204x
31.14x
![Page 93: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/93.jpg)
Ex. 10
222 32)2( xx
10245 2 x
8.2042 x
8.204x
31.14x
9.42)31.14(3
32
xxx
![Page 94: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/94.jpg)
Ex. 10
222 32)2( xx
10245 2 x
8.2042 x
8.204x
31.14x
9.42)31.14(3
32
xxx
feet9.10329.42
![Page 95: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/95.jpg)
Homework
• Page 120
• 21-42 mult. of 3
• 67-77 odd
• 109,124
![Page 96: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/96.jpg)
Lesson Quiz
• Solve by completing the square.1. 01162 xx
523
203
20)3(
91196
116
2
2
2
x
x
x
xx
xx
![Page 97: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/97.jpg)
Lesson Quiz
• Solve by completing the square.2. 0542 xx
1,5
32
9)2(
4544
54
2
2
2
x
x
x
xx
xx
![Page 98: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/98.jpg)
Lesson Quiz
• Solve by using the quadratic formula.3. 0232 2 xx
)2(2
)2)(2(4)3(3 2
21,2
4
253
![Page 99: Quadratic Equations and Applications Objective: To use different methods to solve quadratic equations](https://reader037.vdocument.in/reader037/viewer/2022103022/56649cf75503460f949c6803/html5/thumbnails/99.jpg)
Lesson Quiz
• Solve by using the quadratic formula4. 0243 2 xx
)3(2
)2)(3(4)4(4 2
3
102
6
1024
6
404