Quadratics Unit Test Review
I. Factoring problems – regular, GCF, difference of 2 squares
Factor each quadratic expression (you do not have to “solve for x”)
1. 4x2 – 22
4. 3x2 – 15x – 42
7. x2 + 11x + 28
10. 4x2 – 25
13. x2 + 9x – 22
16. 4x2 + 8x – 60
2. 12x2 + 28
5. x2 – 100
8. x2 + 3x – 28
11. 49x2 – 36
14. x2 – 8x + 12
3. 6x2 -24
6. 25x2 - 9
9. x2 -16
12. x2 – 10x + 21
15. x2 – x – 30
II. For each quadratic function, solve for the zeros (x-intercepts), and identify the axis of
symmetry, the vertex, and the y-intercept. Then sketch a graph of each function.
17. x2 + 15x + 26
19. 16x2 - 4
21. 64x2 – 1
23. 20x2 – 45
18.
20.
22.
24.
x2 – 4x - 32
2x3 + 18x2 + 36x
10x2 – 20x -80
16x2 – 100
25. Solve each of the following equations for x without the use of a calculator. You must use the
quadratic formula for at least one, and factoring for at least one.
a.
x2 + 5x = 0
b. 3x – 5x2 = 0
c.
4x2 – 64 = 0
d. x2 + 6x = 7
e.
2x2 + 8x + 5= 0
IV. Discriminant
For each quadratic equation, a) calculate the value of the discriminant; b) determine if the
discriminant is positive, negative, or zero; and c) state how many (real) solutions the quadratic
equation has. Then sketch a graph of the function.
27. y  x 2  10x  25 = 0
28. y  2x 2  6x  10 = 0
29. y  3x 2  4x  5 = 0
V. Transformations (graphing form/vertex form)
Write each quadratic function in vertex form, y = a(x-h)2 + k. Then identify the transformations
each function makes to the parent function y=x2. Use words like shift up, shift down, shift left,
shift right, flipped, narrower or flatter.
31. y  ( x  2)  3
2
32. y  ( x  2)
33. y  ( x  9)
34. y  4x
2
2
2
35. y  x  3
2
36. y 
1 2
x
3
37. y  2( x  4)
38. y  
2
1 2
x 1
2
39. y  ( x  4)  2
2
VI. Word problems
40. The height of a baseball thrown up into the air is given by the function y = -16t2 + 80t + 6,
where time (t) is measured in seconds and the height (y) is measured in feet.
a) At what time does the ball reach it’s maximum height?
b) What is the ball’s maximum height?
c) When is the ball 42 feet off the ground? (Hint: Once going up, and once coming down.)
41. The Widget Company’s monthly profit, P, is given by the function P = -10x2 + 220x – 50,
where x is the price of each widget the company sells.
a. What is the maximum monthly profit the company can make?
b. How much would the company need to charge for each widget in order to make
the maximum profit?
c. What would their monthly profit be if they set the price of widgets at $9.00?
42. Consider the graph of quadratic function with x-intercepts at (-5,0) and (3,0) that opens upward.
a. Does the graph contain a minimum or maximum and what do you know about its
location?
b. Write two different equations that would be satisfied by the given characteristics.