Chapter 2 Exam Review 1. Sketch the graph of each function, labeling x and y-intercepts (and vertex when appropriate) in each case a.

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f x( ) = x + 3( )2 −1 b.

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f x( ) = x3 + 2x2 − 5x − 6 2. Identify the given quadratic in vertex form:

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f x( ) = −12x − 7 − 2x2

a.

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f x( ) = −2 x − 3( )2 +11 b.

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f x( ) = −2 x − 3( )2 −11

c.

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f x( ) = −2 x + 3( )2 −11 d.

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f x( ) = −2 x + 3( )2 +11 3. Write the vertx-form of the equation of the parabola shown. 4. The demand for balloons depends on the the price per balloon. The number of saw balloons sold, b, is given by

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b p( ) = −2p2 +164 p − 80 , where p is the price per balloon. At what price will the demand for balloons be at a maximum? 5. The height of an arrow shot into the air is given by

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h t( ) = −16t 2 + 48t where

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h t( ) is the height, in feet, of the arrow above the ground t seconds after it is fired. Find the maximum height the arrow reaches. 6. Describe the how the transformations shown in each function change the reference function,

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f x( ) = x2. a.

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f x( ) = −x2 b.

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f x( ) = x2 − 2 c.

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f x( ) = 2 x −1( )2

7. Determine the end behavior of the graph of the polynomial function,

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f x( ) =9x5 + 3x4 + 3

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a.

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as x→−∞, f x( )→∞

as x→∞, f x( )→∞ b.

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as x→−∞, f x( )→∞

as x→∞, f x( )→−∞ c.

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as x→−∞, f x( )→−∞

as x→∞, f x( )→∞

8. Find the zeros of each function below, tell the multiplicity of each zero and describe what happens on the graph of the function at each of those points.

a.

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f x( ) = x3 x − 3( )2 b.

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f x( ) = x3 − 3x + 2 9. Identify the polynomial function that has zeros of

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2, 1, and − 2 and matches the graph provided. a.

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f x( ) = −x3 + x2 + 4x + 4 b.

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f x( ) = −2x2 − x + 2

c.

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f x( ) = x3 + 2x −1 d.

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f x( ) = x3 − x2 − 4x + 4

10. Use long division to find the quotient

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−3x4 −10x3 − 4x2 −11x + 9( ) ÷ x2 + 3x −1( )

11. Use synthetic division to find the quotient

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4x5 + 5x3 − 2x2 − x + 9( ) ÷ x − 2( )

12. Use synthetic division to determine which of the following is NOT a factor of

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f x( ) = x3 + 2x2 − 5x − 6 a.

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x − 3 b.

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x + 3 c.

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x − 2 d.

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x +1 13. Use synthetic division to determine which IS a zero of the given function.

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f x( ) = 3x4 −16x3 − 33x2 +166x +120 a.

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4 b.

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−4 c.

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3 d.

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−5 14. One of the zeros of

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f x( ) = x3 − 6x2 + 5x +12 is

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4 . Find the other two zeros. 15. The area of a rectangle is

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f x( ) = x3 − 3x2 −15x + 25 . If the width is

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x − 5, find the length of the rectangle. 16. Simplify

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i70 a.

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1 b.

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i c.

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−1 d.

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−i 17. Write the expression

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19 + −16 as a complex number. For problems 18, 19, perform the indicated operation and write the result in standard form 18.

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−4 −20 19.

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−4 − 3i( )2 For problems 20, 21, divide and write the result in standard form.

20.

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9 − 2i7 + 3i

a.

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−5758

+4158i b.

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−5758

−4158i c.

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5758

−4158i d.

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5758

+4158i

21.

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−3i3+ 2i( )2

For problems 22, 23, use the quadratic formula to solve.

22.

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4x2 + 5x = −3 a.

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5 ± 23i8

b.

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−5 ± 23i8

c.

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5 ± 73i8

d.

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−5 ± 73i8

23.

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4x2 − 2x + 5 = 0 24. Determine the maximum number of zeros for

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f x( ) = −7x6 + 4x5−2x + 8

25. Use the rational zero test to determine all the possible rational zeros of

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f x( ) = 2x3 + 2x2−2x −12

a.

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±1,±2,±3,±4,±6,±12,± 12,± 32

b.

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±2,±3,±4,±6,±12,±24,± 12,± 32

c.

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±2,±3,±4,±6,±12,± 12,± 32,± 72

d.

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±0,±1,±2,±3,±4,±6,± 12,± 32

26. Identify which of the following third-degree polynomials has the zeros of

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−2 and

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2 + i a.

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P x( ) = x3 − 2x2 − 3x +10 b.

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P x( ) = x3 + 2x2 − 3x −10

c.

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P x( ) = x3 − 2x2 +13x +10 d.

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P x( ) = x3 − 6x2 +13x −10 27. Given that one zero of

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P x( ) = x3 +14x2 + 74x +136 is

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−5 − 3i , find the other two zeros. 28. Find all the zeros for each function below: a.

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P x( ) = x4 − 2x3 − 7x2 +18x −18 b.

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P x( ) = x4 + 8x3 + 8x2 − 72x −153

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x = 3 is a zero( )

29. Determine the domain of

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f x( ) =9x

x x2 −16( )

a.

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−∞,−4( )∪ −4,4( )∪ 4,∞( ) b.

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−∞,4( )∪ 4,∞( ) c.

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−∞,0( )∪ 0,16( )∪ 16,∞( ) d.

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−∞,−4( )∪ −4,0( )∪ 0,4( )∪ 4,∞( ) 30. Graph the following functions. Be sure to label asymptotes and intercepts:

a.

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f x( ) =6x + 65x + 2

b.

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g x( ) =x − 4

x2 − x −12 c.

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h x( ) =x2 − x −12x2 − 4

d.

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j x( ) =x2

x + 4

31. The cost of providing bird flu vaccine to a percent,

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p , of the population of Tucson is given by

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C p( ) =15000p100 − p

, 0 < p < 100

Find the cost of providing the vaccine to 90% of the residents.

32. Choose the partial fraction decomposition for

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−5x2 − 3x − 41

x2 + 9( )2

a.

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5x2 + 9

+3x − 4

x2 + 9( )2 b.

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−5

x2 + 9−3x − 4

x2 + 9( )2 c.

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5x2 + 9

−3x − 4

x2 + 9( )2 d.

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−5

x2 + 9+

3x − 4

x2 + 9( )2

33. Find the partial fraction decomposition for each below:

a.

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9x −15x x − 5( )

b.

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−5x2 − 41x − 64x x + 4( )2