integrated algebra a

1

Name______________________________ Date_______________

Integrated Algebra A Notes/Homework Packet 10

Lesson Homework

Multiplying with Exponents HW #1

Multiplying Monomials HW #2

Distribution & FOIL HW #3

FOIL cont. HW #4

Factoring (GCF) HW #5

GCF cont. HW #6

Difference Between Two Perfect Squares(D2PS) HW #7

Factoring Trinomials HW #8

Factoring Trinomials cont. HW #9

Factoring Trinomials cont. 2 HW #10

Factoring Review HW #11

Graphing Parabolas HW #12

Review

Test

2

Review: Combining Like and Unlike Terms

Give two examples of “like” terms: ___________________

Give two examples of “unlike” terms: ____________________

Like terms have the same _________________ with the same ________________.

Polynomials

A polynomial is named by the number of terms it has.

A monomial has _________ term. Ex: __________________

A binomial has _________ terms. Ex: __________________

A trinomial has _________ terms. Ex: __________________

Combining Like Terms

1. 2x + 5x – 9x = ______________ 2. 22 65 xx = ______________

3. 4x + 5y – 6x + 2y = ______________ 4. x + x + 4a – 5a – x = ________________

5. 32327 xyxy = ______________ 6. xabxab 8452 33 = _______________

7. xxxx 3729 22 = ________________

Multiplying with Exponents

We know that: m2 =

m3 =

So then….. m2 m3 = (m m) (m m m) =

Similarly….. c2 c4 = (c c) (c c c c) =

In general, when x is a number and a and b are positive integers:

xa xb = xa+b

When you multiply numbers with exponents…..

The base remains the same, and then add the exponents.

You must have the same base before you combine the exponents!!!

MULTIPLY – ADD EXPONENTS!!

Example:

x2 x6 = ______________________________ = ____________

54 52 5 = ______________________________ = ____________

3

Practice:

1. x5 x4 = ___________ 5. z3 z4 z5 = ___________

2. x3 x2 = ___________ 6. c c5 = ___________

3. b6 b = ___________ 7. x4 x5 x = ___________

4. m4a m3a = ___________

Dividing with Exponents

x5 x2 can also be written as 2

5

x

x This really means…..

xx

xxxxx

=

In general, when x 0 and a and b are positive integers with a > b:

xa xb = xa – b

When dividing variables with exponents…..

The base remains the same, and then subtract the exponents.

You MUST have the SAME BASE to divide variables with exponents

DIVIDE – SUBTRACT EXPONENTS!!

Simplify the following expressions:

1.x9 x5 = ______ 2. y5 y = ______ 3. c5 c5 = ______

4.3

5

a

a = ______ 5. cy5 cy4 = ______ 6.

a

a

x

x2

5

=______

7.y10b y2b = ______ 8. b

b

a

a = ______

Practice:

1. 26 xx __________ 2. 23 xx ___________ 3. 3yy _________

4. y

y7

__________ 5. 53 xxx __________ 6. 5

5

x

x ____________

4

Name__________________________________ Date________________

HW#1

Combine like terms.

1. 3y + 6x – 6x + y = ______________ 2. 22 216 xx = ______________

3. 5m - 4q + 9 + 2q + 7 = ______________4. 20x2 + 2 + 15x2 - 8 + 3x2 - 4 = _________

5. 6x + 2y + 9 -3x - 5y - 8 = ________________6. x2 + y2 + 8 + 4x2 - 2y2 – 9 = __________

7. x2 + x + x2 + 8x - x = ________________

Simplify the following using the exponent rules:

1. a9 a2 = ______________ 2. a a2 a3 a4 = __________

3. x8 x2 = ___________ 4. k3 k2 = _________

5. k12 k1 = ______________ 6. 9

10

d

d = ____________

7. x7 x3 = ___________ 8. y3 y3 y3 y3 = _________

9. g7m g2m = ______________ 10. h2x h3x h4x = _________

11. x5 x = ___________ 12. a4 a2 = ___________

13. x8 x3 = ______________ 14. d5 d5 d1 = _________

15. x10 x5 = ___________ 16. y5 y2 = ___________

17. d2 d d = ______________ 18. x4 x = ___________

19. x5 x4 = ____________ 20. r2 r4 r5 = _________

21. 2

4

d

d = ____________ 22. x4 x2 x = ______________

Review:

1. What would the equation of the horizontal line be that goes through the point (-4, 1)?

2. Put the following equations into y = mx + b form. (Solve for y).

a. 1532 yx b. xy 35

5

Multiplying Monomials

Procedure:

1. Multiply the coefficients

2. Multiply powers with same base by ________________ EXPONENTS

3. Combine your answers from step 1 and 2

Ex 1: (8x)(3x) _____________ Ex 2: (4x)(8y) ____________

Ex 3: (-4x3y2)(-2xy5) ____________ Ex 4: )2xy)(y5x( 232 (x3) ____________

Practice:

1.(3x)(2x) = _________________ 5.(8d2)(7d5) = _________________

2.(4x2)(3y) = _______________ 6.(10k7)(k4) = __________________

3.(2a4)(5a3) = ______________ 7.(–5hg3)(4h5g5)(-hg) = _________________

4.(5y5)(3y)(2y6) = ______________ 8.(16ab2)(2a2)(-2a4b) = _________________

Dividing Monomials

Procedure:

1. Divide the coefficients

2. Divide powers with same base by ________________ EXPONENTS

(If you get anything to the zero power, it cancels and goes away)

3. Combine your answers from step 1 and 2.

Example 1: Divide 2

5

3a

24a

=_________ Example 2: Divide

32

53

y5x

y20x-

=______

Practice:

1. 2

12

r

r = __________________ 4.

2

23

4

88

xy

yx

= __________________

2. 3

8

c

c = __________________ 5. xt

ytx

42

3 2

= __________________

3. st13

str52 32

= __________________ 6. 11

15

121

11

y

y = __________________

6

Name__________________________________ Date________________

HW#2

More on next page

7

Divide the following:

1. 2

18x = __________ 2.

7

14 22

yx = ___________

3. 2

10

6

36

y

y = __________ 4.

x2

x18 2

= ____________

5. 3

32

5

5

y

yx

= __________ 6.

22

34

7

49

bc

bc = _________

7. xy

yx

3

24 2

= __________ 8.

abc

abc

8

56= __________

Review:

1. A triangle has a leg that measures 6m and a hypotenuse that measures 9m.

Determine the length of the other leg.

2. Solve the inequality and graph the solution.

–2y + 8 26

8

Multiplying a Monomial by a Polynomial

(Review of the Distributive Property)

When multiplying polynomials just use the distributive property!! Don’t forget to

combine all like terms in the end.

Let’s Practice:

1. –5(4m – 6n) = 7. –8(4r – 4

1k) =

2. –5c2(15c – 4c2) = 8. 5(d – 3 + d2) =

3. 4(3e – 5) = 9. -3(2x – 1) =

4. 5x(3x – 4) = 10. -2(2x2 – 3x) =

5. 13x3(5x4 – 2x) = 11. 2x(x2 + 3x – 4) =

6. -(3x – 7) = 12. -2x2(4x – x4) =

Multiplying a Binomial by a Binomial

DOUBLE DISTRIBUTING

“F-O-I-L”

We use this expression to describe how to multiply two binomials.

This is VERY similar to the method of DISTRIBUTION.

Example: (x + 3)(x + 6)

F ________ : x x = (multiply the first two terms in the parentheses)

O ________ : x 6 = (multiply the two outer terms)

I ________ : 3 x = (multiply the two inner terms)

L ________ : 3 6 = (multiply the two last terms in the parentheses)

After this is complete, simplify, by combining like terms together to make a

polynomial: x2 + 6x + 3x + 18 = F O I L

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More Examples:

1. (x + 2)(x + 3) 2. (x – 4)(x – 2)

3. (x2 – 6)(x + 5) 4. (2x + 5)(3x – 4)

Binomials that have the same letters and variables, in the same order, but

different middle signs are called _____________. They are unique, because when

you FOIL them the middle terms cancel each other out.

5. (x + 7)(x – 7) 6. (4x – 3)(4x +3)

Practice:

1. (x + 6)(x + 1) ____________________ = ____________________

2. (x – 5)(x – 3) ____________________ = ____________________

3. (x + 5)(x – 5) ____________________ = ____________________

4. (x2 – 5)(2x – 4) ____________________ = ____________________

5. (5x – 2)(3x – 1) ____________________ = ____________________

6. (2x + 9)(3x2 + 1) ____________________ = ____________________

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Name__________________________________ Date________________

HW#3

Simplify the following using the distribute property:

1. (8xy)(3xz) = _______________ 2. )2xy)(y5x( 232 = _______________

3. –5(4m – 6n) = _______________ 4. 5c2(15c – 4c2) = _______________

5. m3(6m – 3m4) = _______________ 6. a(a +1) = _______________

7. 5m3(–2 + 3m – 4m2) = ______________ 8. 5(d – 3 + d2) – 10d = _____________

Multiply the following using FOIL. Write your answer in simplest form.

1. (x + 1)(x + 2) = _____________________ 2.(x – 3)(x + 4) = ____________________

3. (x + 3)(x – 4)= _____________________ 4. (x2 – 1)(x + 2)= ___________________

5. (2x – 3)(x + 4)= _____________________ 6. (x + 5)(x – 5)= ___________________

7. (4 – x)(4 + x) = _____________________ 8. (3 – 2x2)(1 + x)= __________________

Review:

1. Simplify : a. 322723 b. 8452

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FOIL – Day 2

When squaring terms in parentheses you must square the ENTIRE term, which means

that you must write it TWICE!!!

Then use FOIL to complete the problem!

(2x + 3)2 = (2x + 3)(2x + 3) = =

Practice:

1. (a + 3)2 2. (3x – 2)2

3. (y + 2)2 4. (2x – 1)2

Review:

1. (x + 8)(x + 2) 2. (x – 4)(x – 5)

____________________ ____________________

3. (x + 11)(x – 8) 4. (x + 6)(x – 6)

____________________ ____________________

5. (x – 3)(2x – 2) 6. (2x + 13) 2

____________________ ____________________

12

Multiplying a Binomial by a Polynomial

When you multiply a monomial by a polynomial, you use “double distribution.”

Every term in the monomial needs to get multiplied by every term in the

polynomial.

Example 1: (x + 2)(x2 + 2x + 1) Example2: (x +3)(x2 – 6x – 1)

Example 3: (2x – 1)(3x2 +2x + 2) Example 4: (3x – 2)(-x2 +4x – 8)

Practice:

1. )3x3x)(1x( 2 2. )5x7x)(4x( 2

3. )3x4x)(6x( 2 4. )6x9x2)(5x( 2

5. )6x2x)(1x3( 2 6. )3x5x3)(1x4( 2

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Name__________________________________ Date________________

HW#4

Show work on next page

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1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

15

Factoring (Greatest Common Factor)

Greatest Common Factor (GCF) - of two (or more) integers is the largest integer

that is a factor of both (or all) numbers.

Factoring is like ___________________ the ___________________ __________________.

Steps for factoring using a GCF:

1) Find the ______________ ____________ or __________ that can be ______________

out of each term in the polynomial.

2) Place that number ______________ of a set of ______________________.

3) ______________ ____________ ___________ by that number or letter and

__________those ______________in the parentheses separated by + and - signs.

Examples:

1. 2x + 4 = _________ 2. 5y + 25 = ___________ 3. 4a – 16 = ____________

4. ab + ac = __________ 5. xy – xz = ____________ 6. 7ab + 7c = ___________

7. 5c – 30 = ____________ 8. 6x + 8y = ____________ 9. 18x + 24y = ___________

10. 15a + 12b + 6c = ___________________ 11. x3 + x2 + x =____________________

12. 49 yy = ______________________ 13. 35 x3x = ______________________

Practice:

1. x2y + 2y = ___________________ 2. 5x + 15 = ___________________

3. mn – mp = ___________________ 4. 3x – 15c = ___________________

5. 4x – 6y = _____________________ 6. 7h – 7 = _____________________

7. z4y16x10 = ___________________ 8. 46 a3a = ___________________

16

Name__________________________________ Date________________

HW#5

Factor the following using GCF.

1. 3x + 6 = _________ 2. 10y + 30 = ___________ 3. 5a – 15 = ____________

4. cd + ce = __________ 5. gh – gk = ____________ 6. 4ab + 4c = ___________

7. 3c – 30 = ___________ 8. 10a + 8b + 4c = __________ 9. 18p + 9g = ___________

10. 2x3 + 3x2 + 4x = _______________ 11. 121a - 11b = ___________________

12. z3 + 4z2 = _____________ 13. m4 + m7 = __________

Review:

1. Solve the inequality and graph on a number line.

a. 813 x b. 76 x

2. Solve for the x. Round to the nearest tenth.

a. b.

x

10

15

x

7 37

17

Greatest Common Factoring – Day 2

Review: Factor each of the following.

1. 6x – 18 = _______________ 2. 6y + 15z = ______________

3. 2ab + 7a = _____________ 4. 4p – 4 = ________________

When looking for a common factor, you want to find the greatest factor. That

may included more than just a number or letter. It could include a combination

of both.

Example1: 2xa + 2xb = _____________ Example2: 22 x6yx3 = _________________

Example 3: hg8g4 22 = ____________ Example4: x9x6 2 = __________________

Practice: Factor each of the following.

1. 14mn+14mj = __________________ 2. 6xy – 6xz = _____________________

3. 5gh – 15gk = ___________________ 4. xy40yx10 2 = ___________________

5. 22 b8cb24 = ____________________ 6.

2x2y3 5x3y2= __________________

7. 324 ba16ab12 = _________________ 8. x10x6x2 23 = _________________

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Name__________________________________ Date________________

HW#6

More on next page

19

Review:

1. Solve for x. Round to the nearest tenth.

2. Graph the following equation using the slope-intercept method.

2x + y = 6

m = _______ y-int = ________

3. Determine the image and the quadrants of the given points after a

translation.

Image Quadrant

a. (4, 0) T3, –4 _____________ _____________

b. (–1, 1) T2, –1 _____________ _____________

c. (–3, 5) T3, –5 _____________ _____________

d. (–10, 3) T–2, –2 _____________ _____________

e. (8, –2) T3, –4 _____________ _____________

x

40

15cm

20

Only works with 2

terms that are

Perfect Squares and

being Subtracted

Difference Between 2 Perfect Squares

(D2PS)

EVERY PART OF THE EXPRESSION MUST

REPRESENT A PERFECT SQUARE TO USE THIS METHOD

EXAMPLES OF PERFECT SQUARES to Identify

NUMBERS

12

22

32

42

52

62

72

82

92

102

VARIABLES with Even Exponents

x 2

x 4

a6

VARIABLES with Both

x 2

25y4

16b6

Steps:

1. Use two sets of parentheses

1 set of ( ) with a + sign, the other with a – sign

( – ) ( + )

2. Take the square root of both terms.

3. The square root of the first term is placed first in each parenthesis

4. The square root of the second term is placed second in each

parenthesis

Example1:

x2 – 4

Step 1: ( + )( – )

Step 2:

4

x2

Step 3&4: ( + )( – )

Divide even exponent by 2

21

Example2: Example3:

a6 - b2 25 – 16x2

Step 1: ( + )( – ) Step 1: ( + )( – )

Step 2:

2

6

b

a Step 2:

2x16

25

Step 3&4: ( + )( – ) Step 3&4:( + )( – )

Practice:

Factor the following using D2PS.

1. y2 – 1 2. x2 – 64

_______________________ _______________________

3. 1 – 49x2 4. h2 – 16

_______________________ _______________________

5. 100r2 – 9 6. 36 – n2

_______________________ _______________________

7. 144 – 9g2 8. 4g2 – 81h2

_______________________ _______________________

9. 25c2 – 64d2 10. 9x2 – 16

_______________________ _______________________

11. c2 – d10 12. q6 – p6

_______________________ _______________________

22

Name_____________________________ Date_______________

HW #7


1. k2 – 64 2. 81n2 – 100

_______________________ _______________________

3. 25 – r2 4. 36k2 – 49m2

_______________________ _______________________

5. 16n2 – 9 6. 49 – 100k2

_______________________ _______________________

7. n2 – 4m2 8. z2 – y2

_______________________ _______________________

9. 9x6 – 16y14 10. 36 – y2

_______________________ _______________________

Review:

Factor the following using GCF

11. 3x2y + 12xy 12. 12x + 6y

_______________________ _______________________

13. 4k3 – 36k2 14. math – chat

_______________________ _______________________

23

Factoring Trinomials

There are _______ terms in a trinomial,

so we will use a _______ column table to determine the factors of a trinomial.

STEPS: 1. Use two sets of parenthesis

2. Determine the square root of the first term and place it first in each

parenthesis

3. Determine two numbers that multiply to equal the last term

4. Add the factors together to find the coefficient of the middle term

5. Place these two factors second in each parenthesis

Remember factors must:

Multiply to equal the Last term

&

Add to equal the Middle term

If the last term is + (positive)

Both factors will be the same sign

The sign is determined by the sign of the middle term

Ex 1: x2 + 2x + 1

Ex 2: x2 – 10x +9

Ex 3: x2 + 7x + 10 Ex 4: y2 – 8y + 16

_________________________ _________________________

Add to be: ______ LIST

Multiply to be: ______



_________________________ _________________________





24

Ex 5: x2 + 4x + 3 Ex 6: y2 – 5y + 4

***You can check factoring by performing FOIL***

Check Example 5

Practice:

Factor the following using trinomial.

1. m2 + 9m + 18 2. x2 + 10x + 24

_______________________ _______________________

3. x2 – 15x + 36 4. x2 + 5x + 4

_______________________ _______________________

5. d2 – 14d + 48 6. x2 – 9x – 36

_______________________ _______________________

_________________________ _________________________













25

Name_____________________________ Date_______________

HW #8


1. x2 + 6x + 8 2. x2 – 10x + 21

_______________________ _______________________

Check Solution using FOIL Check Solution using FOIL

3. x2 – 13x + 36 4. c2 + 5c + 6

_______________________ _______________________

5. a2 + 6a + 9 6. c2 - 18c + 17

_______________________ _______________________

7. x2 - 8x + 12 8. b2 + 12b + 11

_______________________ _______________________

Review:


9. x2 – 4 10. z2 – 4y2

_______________________ _______________________

11. 4x6 – y14 12. 49 – y2

_______________________ _______________________

13. Simplify 182 14. Simplify 243

26

Factoring Trinomials continued…


Multiply to equal the Last term

&

Add to equal the Middle term

If the last term is

(negative)

One factor will be positive One factor will be negative The sign of the middle term determines the location of the larger number

Ex 1: x2 + 2x – 15

Ex 2: x2 – 17x – 18

Ex 3: x2 + 11x – 12 Ex 4: x2 – 9x – 90

Ex 5: x2 + 3x – 10 Ex 6: x2 – 6x – 7

***You can check factoring by performing FOIL***

Check Example 5





_________________________ _________________________





_________________________ _________________________





_________________________ _________________________

27

Practice:


1. b2 + 5b – 24 2. m2 – 4m – 77

_______________________ _______________________

3. x2 + 6x – 27 4. m2 – 6m – 7

_______________________ _______________________

5. c2 + 12c – 28 6. x2 – 3x – 40

_______________________ _______________________

7. y2 + 3y – 18 8. m2 + 13m – 30

_______________________ _______________________

9. a2 + a – 56 10. x2 – 22x – 75

_______________________ _______________________

28

Name_____________________________ Date_______________

HW #9


1. j2 – 2j – 8 2. x2 – 22x – 75

_______________________ _______________________

Check Solution Check Solution

3. a2 + a – 56 4. x2 – 3x – 40

_______________________ _______________________

5. m2 + 13m – 30 6. y2 + 3y – 18

_______________________ _______________________

7. k2 – k – 30 8. x2 – 6x – 16

_______________________ _______________________

Review:

Factor the following using GCF.

9. 16fg+16gh = __________________

10.

3x2y5 4x5y2 = ___________________

11. 22 xy20xy40yx10 =________________

29

Factoring Trinomials (Day 3)


________ to equal the _______ term

&

______ to equal the _______ term

Practice Factoring Trinomials

1) x2 + 7x + 12

_______________________

2) x2 – 6x + 8

_______________________

3) x2 + 8x – 20

_______________________

4) x2 – 4x – 21

_______________________

5) x2 – 12x + 27

_______________________

6) x2 + 14x – 32

_______________________

30

Practice:


1. j2 – 2j – 8 2. x2 + 7x + 6

_______________________ _______________________

3. y2 + 5y + 6 4. y2 + 4y - 45

_______________________ _______________________

5. x2 – 15x – 100 6. x2 + 3x + 2

_______________________ _______________________

7. x2 + 6x + 8 8. x2 - 5x - 24

_______________________ _______________________

31

Name__________________________________ Date________________

HW#10

1. a2 – 9a + 20 2. c2 + 12c – 28

_______________________ _______________________

3. y2 + 3y – 18 4. m2 + 13m – 30

_______________________ _______________________

5. x2 – 15x + 36 6. x2 – 22x – 75

_______________________ _______________________

7. a2 + a – 56 8. x2 – 3x – 40

_______________________ _______________________

9. x2 – 13x + 36 10. k2 – k – 30

_______________________ _______________________

32

Factoring Review

(GCF, D2PS, Trinomial)

Determine what type of factoring each problem is (GCF, D2PS, or Trinomial) and

then factor it.

1. x3 + x2 2. 8x + 2y

_______________________ _______________________

3. x2 – 13x + 36 4. 121 – x2y2

_______________________ _______________________

5. ab + ac + ab + ac 6. x2 + 11x + 24

_______________________ _______________________

7. x2 – 49 8. x2 – 10x + 21

_______________________ _______________________

33

9. x2 – y2z4 10. x2y – 10xy2

_______________________ _______________________

11. 5x2 – 10xy2 12. y2 + 14y + 45

_______________________ _______________________

13. 25x2 – 36y2 14. y2 + 3y - 40

_______________________ _______________________

34

Name__________________________________ Date________________

HW#11

Factor the following expressions. You must decide whether to use GCF, D2PS or

trinomials.

1. x2 – 13x + 36 2. 3c – 30

_______________________ _______________________

3. k2 – k – 30 4. x2 – 49

_______________________ _______________________

5. 3x + 6 6. 10y + 30

_______________________ _______________________

7. a2 + a – 56 8. x2 – y2z4

_______________________ _______________________

9. cd + ce 10. x2 – 3x – 40

_______________________ _______________________

11. 25x3 – 5x2 12. 5a – 15

_______________________ _______________________

13. 16p2 - 9 14. x2 + 12x + 27

_______________________ _______________________

15. a6 - 4c2 16. 10a + 8b + 4c

_______________________ _______________________

35

Parabolas

The Quadratic Equation is written as: _______________________.

The graph of this equation is called a __________________.

Let’s sketch what a parabola looks like.

We are going to label some of the parts of a parabola.

A parabola can open up (smile) or down (frown). We know this by our

coefficient in front of the x2 term.

If it is positive coefficient, the parabola will open _________ (or __________).

o The turning point will be a ______________.

If it is negative coefficient, the parabola will open ________ ( or _________).

o The turning point will be a ______________.

Let’s decide if the following will open up or down and if their turning point is a

maximum or minimum just by looking at their equations:

OPENS (up or down) TURNING POINT (max or min)

1. y = x2 + 2 __________ _______________

2. y = x2 + 3x + 2 __________ _______________

3. y = -x2 + 4 __________ _______________

4. y = x2 – 8x + 7 __________ _______________

5. y = 3x2 – 4x + 1 __________ _______________

6. y = –x2 + 2 __________ _______________

7. y = x2 – 4x – 3 __________ _______________

8. y = –x2 – 2 __________ _______________

9. y = -2x2 – 6x – 8 __________ _______________

10. y = x2 – 2x __________ _______________

y

x

Word Bank:

Turning Point

Axis of

Symmetry

Roots

36

We can graph parabolas using our calculator.

STEPS:

Enter the equation into y =

Go to the table, Find the turning point and copy down

the xy-table with 3 points above the turning point and 3 points below the

turning point.

Graph the points and label the graph.

Example 1: GRAPH: y = x2 – 8x + 7

Example 2: GRAPH: 3xy 2

Example 3: GRAPH: y = –x2 – 4x – 3

2nd GRAPH

37

Name__________________________________ Date________________

HW#12

Determine if the following will open up or down and if their turning point is a

maximum or minimum.

OPENS TURNING POINT

1. y = -x2 + 4 __________ _______________

2. y = x2 + 2x -1 __________ _______________

3. y = -3x2 + 4 __________ _______________

4. y = 2x2 + 5x + 1 __________ _______________

5. y = 4x2 – 4x __________ _______________

6. y = –3x2 - 6 __________ _______________

7. y = x2 – 4x – 3 __________ _______________

8. y = 3x2 – 2 __________ _______________

9. y = -5x2 +10x __________ _______________

10. y = -x2 – 2 __________ _______________

Graph the following parabolas:

1. y = x2 – 2x 2. y = 2x2 - 4x + 1

integrated algebra a

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