Solving Quadratics Module 3 Review
____________________
Name
Solve by Factoring
1.) x2 – 64 = 0
2.) x2 – 6x – 16 = 0
4.) 2 x 2  3 x  1  0
5.)
x² – 100 = 0
3.) x2 + 3x = 40
6.)
x² + 6x = 0
Solve by Square Roots:
7.) x 2  64
8.) 4 x 2  81
9.) x 2  7  300
10.)
(x – 5)2 = 36
Solve by using the quadratic formula. Note discriminant & describe the nature of the zeros.
11.
x² + 3x + 2 = 0
12.
4x² – 8x = 1
13.
x² + 8x = 0
Solve each equation any way you want. Show your work.
14. x2 + 11x + 18 = 0
15. x2 + 2x + 1 = 15
16. 7x2 – 9x +1 = 0
17.
(x + 2)² = 36
18.
x² – 10x + 25 = 0
19.
x² + 3x + 7 = 0
20.
x² = 36
21.
x² – 6x + 2 = 0
22. x² – 5x + 4 = 0
REASONING:
20.) Explain why x² = -81 DOES NOT have a real solution.
21.) Which method can’t you use to solve this problem? x² – 47 = 0
Circle one:
Factoring
Completing the Square
Quadratic Formula
Explain why:
22.) Which method can’t you use to solve this problem?
Circle one:
Factoring
x² + 7x = 0
Completing the Square
Quadratic Formula
Explain why:
23.) Which method can you use to solve all quadratic equations?
Circle one:
Factoring
Completing the Square
Explain why:
24.) What are the two mistakes in setting up the quadratic formula?
Solve: 2x² – x – 6 = 0
x
 1  (1) 2  4(2)(6)
2(2)
Quadratic Formula
3
25.) Write in radical form and siplify: 2564
4
26.) Write in exponential form: √83
3
and
162
10
and
27.) How do you find the vertex of x2 + 2x – 8?
√𝑥 7
Find it
Find the zeros of this quadratic by factoring
If you graphed this quadratic, would it open up or down?
How do you know?
If you graphed this quadratic, where would the parabola cross the x axis?
If you looked on the graphing calculator’s table, how would you find the roots of this
quadratic?
28.) There is a list of synonyms that are used interchangeably for “solving” a quadratic. What
are they? Find the ______________, ____________, _____________, ____________, __________
29.) Simplify the following:
a. x3 X5 x = ___________
1
3
b. 𝑥 7 𝑥 7 = ___________
c. (2x4) (-3x5) (x6) = ______________
d. (𝑥 5 )3 = ________
e. (3𝑥 2 )4 = __________
f. (7𝑥)0 = ___________
g.
10𝑥 6
h.
5𝑥 4
2𝑥 8
10𝑥 2
=
=
30.) Factor the following:
a. x2 – 12x + 32
b. 6x2 + 13x + 6
c. x2 – 25
d. 12x2 – x – 6
e. 6x2 + 27x – 15
31.) Clean up the following:
a.
b.
−8 ±4√2
2
5 ±10√3
10
32.) Simplify the following:
a. √12 + √48
b. √80
c 4√20
4
e. 3 + √8 - √2 + 3√5 – 4 - 3√5
k. √−169
f. √81𝑥 8 𝑦 12
3
h. (3√2 + 5) (6√2 – 1)
g. √−27
3
1
i. 184
l. √−60
d. (√8 ) ( √9 )
j. (𝑦 2 )2
m. √−27𝑥 3
n. 𝑖 17
o. 𝑖 12
p. 𝑖 2 𝑖 3 𝑖 4
s. (√−8 ) (√−3 )
r. (-2i)(6i)
t. (2 – 3i) (2 + 3i)
v. -5(3 + 2i) – 5(4 + i)
y. (√5 )2 =
q. (3i)2
w.
u. (9 + 5i) + (4 – i)
10𝑥 6 𝑦 4
6+3𝑖
x. √5𝑥 2 𝑤−3
2−𝑖
(2√3 )2 =
z. (√−9) 2 =
(√−40) 2 =
33.) If a postcard has the dimensions (x + 13) inches by (x) inches with the area of 48 in2, state
the quadratic equation that represents this, find the possible value(s) for x, and find
the actual dimensions of the postcard
34.) Match the following quadratics with their roots:
_____ x2 + 5x + 4
a. x = 4, 1
_____ x2 + 5x – 4
b. x = -3, -7
_____ x2 – 5x + 4
c. x =
−5 ± √41
_____ x2 – 5x – 4
d. x =
5 ± √41
_____ (x + 5)2 = 4
e. x = -4, -1
2
2