Download Test Review Name ____________________________________ Per _______ Chapter 2

Test Review
Chapter 2
Name ____________________________________ Per _______
1.
Find the vertex : y  3x 2  18x  9
2.
Find the number of units that produce a maximum revenue, R  330 x  0.3x 2 , where R is the total
revenue in dollars and x is the number of units. Then find the maximum revenue.
3.
Find a quadratic function whose graph opens upward and has x-intercepts at (5, 0) and (–2, 0).
4.
Find a polynomial function with the given zeros: –3, 0, 5i
5.
Factor the polynomial 2 x 3  3x 2  18x  8 completely knowing that (x – 2) is a factor.
6.
Find all the real roots: x 3  13x  12  0 .
7.
Simplify, then write your answer in standard form: 5   9  5i  8  25 .
8.
Solve for x: 3x 2  4 x  2  0 .
9.
Write as a product of linear factors: x 4  29 x 2  100 .


10. Multiply: 6  2i 4  i  .
11. Use synthetic division to find f(-3):
f(x) = 2x4 + 4x3 + x² + 6x – 10
12. Simplify (write in standard form): f ( x) 
3  5i
.
1  3i
13. Find the coordinates of the vertex, y-intercept, and x-intercept of the quadratic. Then sketch the graph of
f ( x)  x 2  5x  24 .
14. The path of an actor jumping off a stage is given by y  
3 2 6
x  x  15 , where y is the height in feet and
7
7
x is the horizontal distance from the end of the stage.
(a) How far from the stage does the actor go out when the actor reaches his maximum height?
(b) What is the maximum height of the path?
(c) How far from the stage will the actor be when the actor hits the floor?
15. Find the intercepts for the graph of the following function:
f ( x)  x 4  6 x 2  9 x
16. Sketch a graph for: f ( x)  x 3  3x 2  10 x .
17. Find all roots (real and complex) of: 3x 4  4 x 3  4 x 2  4 x  1  0 .


18. Simplify, then write your result in standard form: 5   25  3  9  2i  11 .
19. Write the polynomial as a product of linear factors: p( x)  x 4  25 .
20. Divide:
6 x 4  10 x 3  13x 2  5 x  2
2x 2  1
21. Find the vertical asymptotes(s): f ( x) 
1
.
( x  7)( x  6)
22. Find the horizontal asymptote(s)of each:
x2  4
a) f ( x)  2
x  16
23. Find the domain: f ( x) 
7x  5
b) 2
9 x  16
5x 3  2
c) 2
x 4
x5
.
x  6x  5
2
24. Find the domain, x-intercept, y-intercept, vertical and horizontal asymptotes and sketch the graph of
f ( x) 
x5
.
x2
Precalculus, Chapter 2 Test Review Solutions
1. (3,18)
2. 550 units will produce a maximum revenue of $90,750
3. y  x 2  3x  10
4. f ( x)  x 4  3x 3  25x 2  75x
5. ( x  2)(2 x  1)( x  4)
6. 1, 3, –4
7. 8 – 2i
2
2i

3
3
9. ( x  2i)( x  2i)( x  5i)( x  5i)
8.
10. 26 - 2i
11. f(-3) = 35
9 2
 i
5 5
 5 121 
13. V:  , 
 ; x-int: (8, 0), (–3, 0); y-int: (0, –24); graph is a parabola
4 
2

14. a) 1 foot
b) 15 73
c) 7
12.
15. (0, 0) and (3, 0)
16.
17. 1, 13 , i,  i
18. 16 + 2i
19. ( x  5 )( x  5 )( x  5i)( x  5i)
20. 3x 2  5 x  8 
10
2x 2  1
21. x = –7, x = 6
22. a) y = 1
b) y = 0
23. All real numbers except 5 and 1
c) none
24. domain: ARN, x  2
x-int: (–5, 0)
y-int: (0,  52 )
VA: x = 2
HA: y = 1