Algebra 2A
Unit 2 Review
Name: _____________________________________
For numbers 1 – 3, graph the quadratic function. Identify the vertex, y-intercept, and axis of symmetry.
1. f(x) = –x2 + 1
2. f(x) = 3x2 + 6x – 4
3. f(x)= (x – 2)2 + 4
For numbers 4 – 13, solve the quadratic equation by using any appropriate method.
4. 4x2 – 25 = 0
5. 9x2 – 12x + 4 = 0
6. 2x2 – 4x = 0
7. 2x2 + 1 = –15
8. 3(x + 1)2 + 4 = 22
9. x2 – 2x + 20 = 0
10. x2 – 6x + 21 = 0
11. –5x2 + 10x + 20 = 0
12. x2 – 3x = –5
13. 2x2 – 8x + 16 = 0
For numbers 14 – 16, simplify the expression.
14. i + 3 + 4
15. (–5 – 8i) – (–4 – 8i)
16. (2 + i)(5 – 3i)
For numbers 17 & 18, find the discriminant and give the number and type of solutions of the equation.
17. 6x2 = 4 – 5x
18. 2x2 – 3x = –4
For numbers 19 & 20, graph the quadratic inequality.
19. y ≤ 2x2 – 1
20. y > x2 – 6x + 6
21. Write the following equation in vertex form. Then identify the vertex, axis of symmetry, domain, and range: y = x2 + 16x – 21
22. The height h (in feet) of a certain aircraft t seconds after it leaves the ground is modeled by h(t) = –16t2 + 64t + 12.
When will the aircraft reach its maximum height? What will the maximum height be?
23. Ana throws a rock into the air with an initial velocity of 27 feet per second. Her hand is 6 feet above the ground when she throws
the rock.
h = –16t2 + vo t + ho
h = ending height (feet)
t = time (seconds)
vo = initial velocity (feet per second)
ho = initial height (feet)
a) Write a vertical motion model for the height of the rock after it is thrown.
b) Use the model to determine how long the rock remains in the air.
24. Solve 2x2 + 5x – 7 ≤ 0
For numbers 25 – 28, identify in which step, if any, that an error occurred.
25. Find the discriminant of: 3x2 – 5x = 7.
Step 1: a = 3, b = –5, c = 7
Step 2: discriminant = b2 – 4ac = (–5)2 – 4(3)(7)
Step 3: discriminant = –59
26. Solve: 2x2 – 9x = –4
Step 1: 2x2 – 9x + 4 = 0
Step 2: x2 – 9x + 8 = 0
Step 3: (x – 8)(x – 1) = 0
8 
1

Step 4:  x   x    0
2 
2

Step 5: (x – 4)(2x – 1) = 0
Step 6: x – 4 = 0 OR 2x – 1 = 0
1
Step 7: x = 4
OR x 
2
27. Solve: x2 + 8x – 20 = 0
Step 1: x2 + 8x – 20 = 0
Step 2: x2 + 8x = 20
Step 3: x2 + 8x + 16 = 20
Step 4:  x  4   20
2
Step 5: x  4   20
Step 6: x  4  20
28. Solve: 3x2 – 4x – 8 = –6
Step 1: 3x2 – 4x – 2 = 0
Step 2: a = 3, b = –4, c = –2
Step 3: discriminant = b2 – 4ac = (–4)2 – 4(3)(–2)
Step 4: discriminant = 40
Step 5: Use quadratic formula: x 
Step 6: Simplify: x 
4  2 10
6
Step 7: Final answer: x 
2  10
3
4  40
2  3
29. Describe the relationship between y = x2 and y = x2 – 4.
30. Which of the following characteristics (vertex, axis of symmetry, y-intercept, solutions, domain, range, and maximum/minimum )
do the graphs of the following functions have in common?
Function 2: y = –3(x + 4)2 – 4
Function 1: y = x2 + 8x + 12
For numbers 31 – 33, simplify.
31.
8  24
32.
7  12
33.
25  36
34. A graph of a quadratic function has the following points (–6, 0) and (2, 0). Write an equation in the form a𝑥 2 + bx + c = 0, where
a, b, and c are integers.
35. Determine how many solutions an equation has if the graph of the function crosses the x-axis 0 times.
36. Determine how many solutions an equation has if the graph of the function crosses the x-axis 2 times.
37. Write the equation of a quadratic function that has the same zeros as f(x) = x2 – 5x – 24.
For numbers 38 & 39, solve the equation.
38. (x + 12)2 = 19
39. 2(x – 3)2 + 7 = 57
40. Find the values of x and y that make the equation true: 8x – 5i = 2(x + 7) – 15yi true.
41. A ball is thrown downward from a height of 14 feet with an initial velocity of 24 ft/sec. If the ball is caught at a height of 3 feet,
for how long is the ball in the air?