Algebra II
(Quiz Review)
Section 4.5- 4.6 Workday
Name: __________________________
Block: _______
Solve each equation by finding square roots. Remember to include BOTH solutions!
1. x2 – 9 = 0
2. 𝟑𝑥 2 + 2 = 50
3. 𝑥 2 + 15 = 16
4. 2(𝑥 − 5)2  64 = 0
5. 4(𝑥 − 3)2 100 = 0
6. −5(𝑥 + 7)2 + 25 = 0
Real-Life Application:
7. You are painting a large rectangular wall mural. The wall length is 3 times the height. The area of the wall is
300 ft2. Write an equation to represent the area of the wall. Let x represent the height.
Solve your area equation to find the dimensions of the wall. Show your work.
8. A packing box is 4 ft deep. One side of the box is 1.5 times longer than the other. The volume
of the box is 24 ft3. Write and solve an equation to represent this situation. What are the
dimensions of the box?
Solve each equation. Factor the perfect square trinomial and then use the square root method.
9. x2 – 14x + 49 = 81
10. x2 + 6x + 9 = 1
11. 9x2 – 12x + 4 = 49
2
2
(x – 7) = 81
(x + 3) = 1
(3x – 2)2 = 49
12. 4x2 + 36x + 81 = 16
13. x2 + 2x + 1 = 36
14. x2  16x + 64 = 9
Complete the Square to make a perfect square trinomial. Then, rewrite the expressions as a squared
binomial.
15. x2 + 8x +
( ________)2
18. x2 – 24x +
( ________)2
16. x2 –20x +
17. x2 – 14x +
( ________)2
( ________)2
20. x2 – 46x +
19. x2 + 34x +
( ________)2
( ________)2
Solve the following equations by completing the square. Show all steps of your work.
Example:
x2 – 8x – 5 = 0
21. x2 + 12x + 9 = 0
2
x – 8x = 5 (make it = c value)
x2 – 8x + 16 = 9 + 16
(x – 4)2 = 25
√(𝑥 − 4)2 = ±√25
𝑥−4 = 5
𝑥 − 4 = −5
+4
+4
+4
+4
x = 9 and x = -1
23. 2x2 +11x  23 = x + 3
22. x2 – 10x = –11
24. 3x2  42x = 78
Complete the square to write the following equations in vertex form. Then give the vertex as an ordered pair.
Show your work!
25. y = x2  18x + 13
26. y = x2 + 32x  8
*27. y = –2x2 + 6x  2 (uses decimals !)
Vertex: ____________
Vertex: ____________
Vertex: ______________
Find the value of k that would make the left side of each equation a perfect square trinomial.
28. x2 + kx + 196 = 0
29. 64x2  kx + 1 = 0
30. x2  kx + 16 = 0
31. 4x2  kx + 9 = 0
Solve each equation by factoring. Check your answers. To start, factor the quadratic expression.
32. 2x2  2x  60 = 0
33. x2  10x = 21
34. 3𝑥 2 + 22𝑥 − 16 = 0
35. x2 = 12x
Write a quadratic equation with the given solutions in STANDARD FORM.
(Remember solutions = zeros = x-intercepts!)
36. x = 6 and 0, a value is -3
37. x = 3 and 8, a value is 2
Solve each equation by graphing. Give each answer to the thousandths place (three
decimal places). Sketch the graph you used and label the solutions.
38. 2x2  x  10 = 0
39. 4x2 + 27x = 12
40. 6x2 = 13x + 28
Real-Life Applications:
x2  25x = 0. If
one end of the street is considered to be x = 0 and the street lies on the x-axis, where else does the path
intersect the street?
41. A parabolic jogging path intersects both ends of a street. The path has the equation
42.
a. How high in the air does the ball go? Show your work!
b. Assume that the tennis player hits the ball on its way back down when it is
0.6m above the point of toss. For how many seconds is the ball in the air
between the toss and the point of contact?
c. Sketch a graph of the function and label all critical points used during this
problem. Label the axes with the appropriate variables (it’s not x and y!).
**Do you know the quadratic formula?
**Can you use it to solve a quadratic equation in standard form??
43. Solve using the Quadratic Formula: 𝟐𝒙𝟐 − 𝟓𝒙 − 𝟑 = 𝟎