Download Ch 8 Exam Review

Ch 8 Exam Review
Note: These are only a sample of the type of problems you may see on the exam.
Solve the equation by the square root property. If
Sketch the graph of the quadratic function. Give the
possible, simplify radicals or rationalize denominators.
vertex and axis of symmetry.
Express imaginary solutions in the form a + bi.
14) f(x) = -(x + 1)2 + 9
2
y
1) 169x = 64
10
2) (x + 5)2 = 14
5
3) (x - 7)2 = -121
-10
-5
Complete the square for the binomial. Then factor the
resulting perfect square trinomial.
4) x2 + 6x
5
10 x
5
10 x
-5
-10
5) x2 - 3x
Solve the quadratic equation by completing the square.
6) 9x2 + 18x + 5 = 0
15) y + 4 = (x - 2)2
y
10
7) x2 - 12x = 5
5
Use the quadratic formula to solve the equation.
8) x2 - 12x + 32 = 0
-10
-5
-5
9) 4x2 + 10x + 2 = 0
-10
10) -7x2 + 3x - 8 = 0
Write a quadratic equation in standard form with the
given solution set.
11) {-10, 3}
16) f(x) = x2 - 9
y
10
12) {3 +
10, 3 -
13) {9 + i, 9 - i}
10}
-10
10
-10
x
Sketch the graph of the quadratic function. Identify the
vertex, intercepts, and the equation for the axis of
symmetry.
17) f(x) = 6 + 5x + x 2
y
5
-5
24) x-2 - 8x-1 = -10
5
10 x
Solve the polynomial inequality and graph the solution
set on a number line.
26) x2 + 2x - 8 > 0
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
-5
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
18) f(x) = -3x2 - 30x - 79
y
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
Solve the rational inequality and graph the solution set
on a real number line.
x- 2 < 0
28)
x+1
10
5
-5
1
27) x2 - 3x - 18 ≤ 0
-10
-10
x - 18 = 0
25) (x2 - 2x)2 - 23(x2 - 2x) + 120 = 0
10
-10
23) 2x - 9
5
10 x
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
-5
29)
-10
Determine whether the given quadratic function has a
minimum value or maximum value. Then find the
minimum or maximum value and determine where it
occurs.
19) f(x) = 3x2 - 3x - 9
x + 25 < 4
x+4
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
30)
1 <1
x-5
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
Solve the problem.
20) You have 312 feet of fencing to enclose a
rectangular region. Find the dimensions of
the rectangle that maximize the enclosed
area.
21) Among all pairs of numbers whose difference
is 82, find a pair whose product is as small as
possible.
Solve the equation by making an appropriate
substitution.
22) x4 - 9x2 + 20 = 0
Answer Key
Testname: CH 8 EXAM REVIEW
8
1) ±
13
2) {-5 ± 14}
3) {7 ± 11i}
4) 9; x2 + 6x + 9 = (x + 3)2
5)
9 2
9
3 2
; x - 3x + = x 4
4
2
1
5
6) - , 3
3
7) {6 ± 41}
8) {4, 8}
9)
10)
-5 ± 17
4
3
± i 215
14
-14
11) x2 + 7x - 30 = 0
12) x2 - 6x - 1 = 0
13) x2 - 18x + 82 = 0
14) vertex: (- 1, 9)
axis of symmetry: x = - 1
y
10
5
-10
-5
5
10 x
5
10 x
-5
-10
15) vertex: (2, - 4)
axis of symmetry: x = 2
y
10
5
-10
-5
-5
-10
Answer Key
Testname: CH 8 EXAM REVIEW
16) vertex: (0, -9)
axis of symmetry: x = 0
y
10
-10
x
10
-10
5
1
17) vertex: - , 2
4
x-intercepts: (-3, 0) and (-2, 0)
y-intercept: (0, 6)
5
axis of symmetry: x = 2
y
10
5
-10
-5
5
10 x
-5
-10
18) vertex: (-5, -4)
x-intercepts: none
y-intercept: (0, -79)
axis of symmetry: x = -5
y
10
5
-10
-5
5
-5
-10
10 x
Answer Key
Testname: CH 8 EXAM REVIEW
19) Minimum is 20) 78 ft by 78 ft
21) -41 and 41
22) {-2, 2, - 5,
23) {36}
24)
39
1
at x = .
4
2
5}
4± 6
10
25) {- 3, - 2, 5, 4}
26) (-∞, -4) ∪ (2, ∞)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
27) [-3, 6]
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
28) (-1, 2)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
29) (-∞, -4) ∪ 3, ∞
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
30) (-∞, 5) ∪ (6, ∞)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0