Algebra 2
Review Chapter 5
1a. Find a quadratic model for the attendance at
women’s college basketball games.
1b. What does your equation predict the
attendance will be in year 10?
Name ________________________________
Year
Attendance
(thousands)
4962
5234
6734
7387
8010
8698
0
1
2
3
4
5
Sketch a graph of the parabola with the given vertex through the given point.
2. vertex (0, 0), point (-3, 3)
3. vertex (1, 3), point (2, 6)
6
8
5
7
4
6
3
2
5
1
-6 -5 -4 -3 -2 -1
-1
4
1 2 3 4 5 6
3
-2
2
-3
1
-4
-5
-3
-2
-1
-6
1
-1
Graph each quadratic function. Identify the axis of symmetry and the coordinates of the vertex.
4. y = x2 – 7
5. y = x2 + 2x + 6
-8
-6
-4
8
8
6
6
4
4
2
2
-2
2
4
6
8
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8
6
8
Write each function in vertex form. Sketch the graph of the function and label its vertex.
6. y = x2 – 2x - 3
7. y = -x2 + 2x + 2
-8
-6
-4
8
8
6
6
4
4
2
2
-2
2
4
6
8
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
2
3
Factor.
8. x2 – 7x
9. x2 + 2x – 8
10 2x2 + 7x – 9
Solve the quadratic equation.
12. 3x2 – 14x + 8 = 0
13. x2 + 8x + 16 = 0
15. 3x2 + 4x – 10 = 0
16. x2 + 3x + 5 = 0
11. x2 – 3x – 4
14. x2 – 9 = 0
17. For a model rocket, the altitude h, in meters, as a function of time t, in seconds, is give by h = 68t – 4.9t2. Find the maximum
height of the rocket. How long does it take to reach the maximum height?
Simplify each expression.
18. (3 + 4i) – (7 – 2i)
19. (5 – i)(9 + 6i)
20. (3 + 8i) + (5 – 2i)
Find the additive inverse of each number.
21. 2 – i
22. -4 + 3i
Find the absolute value of each complex number.
23. 7 – 2i
24. 8i
Evaluate the discriminant of each equation. How many real and imaginary solutions does each have?
25. x2 + 6x – 7 = 0
26. 3x2 – x + 3 = 0
Write the equation of the parabola in vertex form.
27.
28.
6
2
5
1
4
-6
-5
-4
-3
-2
-1
1
3
-1
2
-2
1
-3
-1
1
2
3
4
5
-4
6
-1
-5
-2
-6
Solve by completing the square. Show your work on another sheet of paper.
29. x2 - 3x = 28
30.
x2 – 3x – 4 = 0
2