Algebra 2
Study Guide Chapter 5
Directions: Show all work and reasoning to receive full credit.
Name ____________________________
Identify the quadratic, linear and constant terms. Determine whether each function is linear or quadratic.
1. f(x) = 7(x – 2) + 5(3x)
2. y = (2x – 3)(x + 2) – 2x2
Identify the vertex and axis of symmetry.
3
3.
5
4.
2
4
Vertex:
1
-1
1
2
3
4
5
6
7
8
9
2
-1
-2
Vertex:
3
1
Axis of Symmetry:
Axis of Symmetry:
-3
-4
-4
-3
-2
-1
1
2
3
4
-1
-5
-6
-2
-7
-3
For problems 5 and 6:
a) Write each function in vertex form. SHOW ALL WORK.
b) Graph each function using its vertex and y – intercept (which will be evident from vertex form).
5. y = x2 – 2x – 3
6. y = -x2 + 2x + 2
Vertex:
Vertex:
y – intercept:
y – intercept:
-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
Graph each quadratic function using the requested information.
7. y + 7 = x2
8. y = x2 + 2x + 6
Up or down (answer only):
Vertex (work and answer):
Up or down (answer only):
Vertex (work and answer):
y – intercept (answer only):
y – intercept (answer only):
-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
9a. Use your graphing calculator to find a quadratic model for the attendance at
men’s college basketball games starting in 1960 (year 0).
9b. What does your equation predict the attendance will be in year 10?
Factor each quadratic expression completely.
10. x2 – 7x
11. x2 + 2x – 8
12 2x2 + 7x – 9
Factor and solve each quadratic equation.
14. 3x2 – 14x + 8 = 0
15. x2 + 8x + 16 = 0
4
Year
1960
1961
1962
1963
1964
1965
6
8
Attendance
(thousands)
4962
5234
6734
7387
8010
8698
13. 25x2 – 81
16. x2 – 9 = 0
Simplify each expression.
17.
 120
20. (3 + 4i) – (7 – 2i)
18. (  12 )( 8 )
19. (-i + 3)(2i – 1)i
21. (5 – i)(9 + 6i)
22. (3 + 8i) + (5 – 2i)
Find the additive inverse of each number.
23. 2 – i
24. -4 + 3i
25. Find the absolute value of the complex numbers. Graph the Point
a. 7 – 2i
b. -4 + 8i
Imaginary
Imaginary
10
10
8
8
6
6
4
4
2
-10 -8
-6 -4
-2
2
2
4
6
8 10
Real
-2
-10 -8
-6 -4
-2
2
-2
-4
-4
-6
-6
-8
-8
-10
-10
Solve by using the Quadratic Formula.
26. 3x2 + 4x – 10 = 0
27. x2 + 3x + 5 = 0
Evaluate the discriminant of each equation. How many real and/or imaginary solutions does each have?
28. x2 + 6x – 7 = 0
29. 3x2 – x + 3 = 0
4
6
8 10
Real
Solve by completing the square.
30. x2 + 6x – 7 = 0
31.
16x2 - 8x + 4 = 0
32. For a model rocket, the altitude h, in meters, as a function of time t, in seconds, is give by h = 68t – 4.9t2.
(a) How much time does it take to reach the maximum height?
(b) Find the maximum height of the rocket.
33. A lighting fixture manufacturer has daily production costs of C  0.25n
dollars and n is the number of light fixtures produced.
(a) How many fixtures should be produced to yield a minimum cost?
2
 10n  800 , where C is the total daily cost in
(b) What is the minimum cost?
34. Find a quadratic function that includes the values in the table. Show your system of equations, your matrices, and the final
quadratic function.
x
-1
2
3
y
12
3
4
10
8
35. Solve the quadratic equation by graphing on your calculator.
6
8x2 – 5x = 4
4
2
Sketch your graph to the right.
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10