![Page 1: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/1.jpg)
Math I
UNIT QUESTION: What is a quadratic function?Standard: MM2A3, MM2A4
Today’s Question:How do you solve quadratic equations that can’t be factored?Standard: MM2A4.b.
![Page 2: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/2.jpg)
DAY ONE
![Page 3: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/3.jpg)
3.6 - Solving a Quadratic Equation by Square Roots
![Page 4: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/4.jpg)
Let’s look at some examples where x2 is already by
itself.
![Page 5: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/5.jpg)
Examples. Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions.
5.24.1 22 nx
42 x 52 n
5n2x
![Page 6: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/6.jpg)
10.425.311.2811.
:You try2222 xcyx
![Page 7: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/7.jpg)
Let’s look at some examples where
x2 is NOT by itself.
![Page 8: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/8.jpg)
0483 2 xWe must solve to get x2 by
itself 1st!
483 2 x
162 x
4x
![Page 9: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/9.jpg)
96322 xWe must solve to get x2 by
itself 1st!
642 x
8x
![Page 10: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/10.jpg)
You try!
0722 01 22 xx
![Page 11: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/11.jpg)
Falling object model
When an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model:
sth 216
![Page 12: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/12.jpg)
An engineering student is a contestant in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking (s = starting height). Find the time (t) it will take for the egg to hit the ground (height = ? ). Disregard air resistance.
SOLUTION: The starting height is 32 feet.
Now, substitute 0 for h and solve.32160 2 t21632 t Subtract 32 from both sides
Divide both sides by –16 22 tTake the square root of both sides
4.12 t So, the answer is 1.4 seconds. It is only the positive of the square root b/c you can’t have negative seconds!!!!!
sth 216
![Page 13: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/13.jpg)
DAY TWO
![Page 14: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/14.jpg)
The following quadratics are in standard form, ax2 + bx + c
Evaluate b2 – 4ac for each of the following
1
0
-15
1)x2 – 3x + 2
2)x2 – 4x + 4
3)2x2 – 3x + 3
![Page 15: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/15.jpg)
There is a way to tell how many roots an equation will have.
It’s called finding the discriminant.
The discriminant is a small part of the quadratic formula.
b ac2 4
![Page 16: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/16.jpg)
b ac2 4If the answer is POSITIVE, then you will have 2 roots.
If the answer is ZERO, then you will have 1 root.
If the answer is NEGATIVE, then you will have no roots.
Our text book says solutions instead of roots (same thing).
![Page 17: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/17.jpg)
Determine the number of roots.
Example: 1
0432 xx
b ac2 4 ( ) ( )( )3 4 1 42
9 16 7
![Page 18: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/18.jpg)
Determine the number of roots.
Example: 2
0442 xx
b ac2 4 ( ) ( )( )4 4 1 42
16 160
![Page 19: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/19.jpg)
Determine the number of roots.
Example: 3
0452 xx
b ac2 4 ( ) ( )( )5 4 1 42
25 169
![Page 20: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/20.jpg)
Find the number of x-intercepts.Example: 4
342 xxy
b ac2 4 ( ) ( )( )4 4 1 32
16 124
![Page 21: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/21.jpg)
Find the number of x-intercepts.Example: 5
322 xxy
b ac2 4 )3)(1(4)2( 2 124
8
![Page 22: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/22.jpg)
Solve for x:
2 25 0x
2 9 14 0x x
![Page 23: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/23.jpg)
Quadratic Formula: gives the solution of in terms of the coefficients a, b & c.
2 0ax bx c
a
acbbx
2
42
a
The solutions of the quadratic equation are
a
a
c
c
bb
b
![Page 24: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/24.jpg)
Ex: 1 Solve x2+ 9x +14 = 0
a
acbbx
2
42
a =
b =
c =
12
141499 2
1st
12
1414819
2nd
2
56819
2
259
2
59
2
59
2
59 and
2
14
2
4 and 7 2 and
![Page 25: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/25.jpg)
2 4 3 0x x
![Page 26: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/26.jpg)
2
2
2
1.)2 10 0
2.) 3 4 0
3.)2 3 8
x x
x x
x x
-5/2 & 2
-1 & 4
2.89 & -1.39
![Page 27: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/27.jpg)
A rocket is shot upward with an initial velocity of 125 feet per second from a platform 3 feet above the ground. Use the model to find how long it will take the rocket to hit the ground.
216h t vt s
3 ft
t = 7.83 seconds
![Page 28: Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?](https://reader036.vdocument.in/reader036/viewer/2022062511/551b7bb1550346167e8b478d/html5/thumbnails/28.jpg)
HOMEWORK