chapter 2 exam review - tucson unified school...
Post on 03-Jun-2018
219 Views
Preview:
TRANSCRIPT
Chapter 2 Exam Review 1. Sketch the graph of each function, labeling x and y-intercepts (and vertex when appropriate) in each case a.
€
f x( ) = x + 3( )2 −1 b.
€
f x( ) = x3 + 2x2 − 5x − 6 2. Identify the given quadratic in vertex form:
€
f x( ) = −12x − 7 − 2x2
a.
€
f x( ) = −2 x − 3( )2 +11 b.
€
f x( ) = −2 x − 3( )2 −11
c.
€
f x( ) = −2 x + 3( )2 −11 d.
€
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
€
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
€
h t( ) = −16t 2 + 48t where
€
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,
€
f x( ) = x2. a.
€
f x( ) = −x2 b.
€
f x( ) = x2 − 2 c.
€
f x( ) = 2 x −1( )2
7. Determine the end behavior of the graph of the polynomial function,
€
f x( ) =9x5 + 3x4 + 3
6
a.
€
as x→−∞, f x( )→∞
as x→∞, f x( )→∞ b.
€
as x→−∞, f x( )→∞
as x→∞, f x( )→−∞ c.
€
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.
€
f x( ) = x3 x − 3( )2 b.
€
f x( ) = x3 − 3x + 2 9. Identify the polynomial function that has zeros of
€
2, 1, and − 2 and matches the graph provided. a.
€
f x( ) = −x3 + x2 + 4x + 4 b.
€
f x( ) = −2x2 − x + 2
c.
€
f x( ) = x3 + 2x −1 d.
€
f x( ) = x3 − x2 − 4x + 4
10. Use long division to find the quotient
€
−3x4 −10x3 − 4x2 −11x + 9( ) ÷ x2 + 3x −1( )
11. Use synthetic division to find the quotient
€
4x5 + 5x3 − 2x2 − x + 9( ) ÷ x − 2( )
12. Use synthetic division to determine which of the following is NOT a factor of
€
f x( ) = x3 + 2x2 − 5x − 6 a.
€
x − 3 b.
€
x + 3 c.
€
x − 2 d.
€
x +1 13. Use synthetic division to determine which IS a zero of the given function.
€
f x( ) = 3x4 −16x3 − 33x2 +166x +120 a.
€
4 b.
€
−4 c.
€
3 d.
€
−5 14. One of the zeros of
€
f x( ) = x3 − 6x2 + 5x +12 is
€
4 . Find the other two zeros. 15. The area of a rectangle is
€
f x( ) = x3 − 3x2 −15x + 25 . If the width is
€
x − 5, find the length of the rectangle. 16. Simplify
€
i70 a.
€
1 b.
€
i c.
€
−1 d.
€
−i 17. Write the expression
€
19 + −16 as a complex number. For problems 18, 19, perform the indicated operation and write the result in standard form 18.
€
−4 −20 19.
€
−4 − 3i( )2 For problems 20, 21, divide and write the result in standard form.
20.
€
9 − 2i7 + 3i
a.
€
−5758
+4158i b.
€
−5758
−4158i c.
€
5758
−4158i d.
€
5758
+4158i
21.
€
−3i3+ 2i( )2
For problems 22, 23, use the quadratic formula to solve.
22.
€
4x2 + 5x = −3 a.
€
5 ± 23i8
b.
€
−5 ± 23i8
c.
€
5 ± 73i8
d.
€
−5 ± 73i8
23.
€
4x2 − 2x + 5 = 0 24. Determine the maximum number of zeros for
€
f x( ) = −7x6 + 4x5−2x + 8
25. Use the rational zero test to determine all the possible rational zeros of
€
f x( ) = 2x3 + 2x2−2x −12
a.
€
±1,±2,±3,±4,±6,±12,± 12,± 32
b.
€
±2,±3,±4,±6,±12,±24,± 12,± 32
c.
€
±2,±3,±4,±6,±12,± 12,± 32,± 72
d.
€
±0,±1,±2,±3,±4,±6,± 12,± 32
26. Identify which of the following third-degree polynomials has the zeros of
€
−2 and
€
2 + i a.
€
P x( ) = x3 − 2x2 − 3x +10 b.
€
P x( ) = x3 + 2x2 − 3x −10
c.
€
P x( ) = x3 − 2x2 +13x +10 d.
€
P x( ) = x3 − 6x2 +13x −10 27. Given that one zero of
€
P x( ) = x3 +14x2 + 74x +136 is
€
−5 − 3i , find the other two zeros. 28. Find all the zeros for each function below: a.
€
P x( ) = x4 − 2x3 − 7x2 +18x −18 b.
€
P x( ) = x4 + 8x3 + 8x2 − 72x −153
€
x = 3 is a zero( )
29. Determine the domain of
€
f x( ) =9x
x x2 −16( )
a.
€
−∞,−4( )∪ −4,4( )∪ 4,∞( ) b.
€
−∞,4( )∪ 4,∞( ) c.
€
−∞,0( )∪ 0,16( )∪ 16,∞( ) d.
€
−∞,−4( )∪ −4,0( )∪ 0,4( )∪ 4,∞( ) 30. Graph the following functions. Be sure to label asymptotes and intercepts:
a.
€
f x( ) =6x + 65x + 2
b.
€
g x( ) =x − 4
x2 − x −12 c.
€
h x( ) =x2 − x −12x2 − 4
d.
€
j x( ) =x2
x + 4
31. The cost of providing bird flu vaccine to a percent,
€
p , of the population of Tucson is given by
€
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
€
−5x2 − 3x − 41
x2 + 9( )2
a.
€
5x2 + 9
+3x − 4
x2 + 9( )2 b.
€
−5
x2 + 9−3x − 4
x2 + 9( )2 c.
€
5x2 + 9
−3x − 4
x2 + 9( )2 d.
€
−5
x2 + 9+
3x − 4
x2 + 9( )2
33. Find the partial fraction decomposition for each below:
a.
€
9x −15x x − 5( )
b.
€
−5x2 − 41x − 64x x + 4( )2
top related