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Quadratics part 2

Total questions: 95

Worksheet time: 5hrs 8mins

Name
Class
Date
1.
In the equation
y = x2 +5x +7, match each leading coefficient with its correct letter 
a)
a=0, b=5, c=7
b)
a=1, b=5, c=7
c)
a=7, b=5, c=1
2.
What should you do first in solving this equation?
x2 + 6x - 13 = 3
a)
Get factored form
b)
Write down: a=1, b=6, c=-13
c)
Make it equal 0 by subtracting 3 on each side
d)
Type it all in a calculator.
3.
Determine the values of
a, b, and c for
the quadratic equation: 
4x2 – 8x = 3
a)
a = 4, b = -8, c = 3
b)
a = 4, b =-8, c =-3
c)
a = 4, b = 8, c = 3
d)
a = 4, b = 8, c = -3
4.

Solve 3x2 - 11x + 10 . USE THE QUADRATIC FORMULA

a)

1.7 and 2

b)

1 and 2

c)

1.5 and 2

d)

-1.7 and 2

5.
Factor:
x2 + 5x - 24
a)
(x - 8)(x + 3)
b)
(x + 8)(x - 3)
c)
(x + 6)(x - 4)
d)
(x + 12)(x - 2)
6.
Find the factors of 4x2-16x-9
a)
(2x-9)(2x+1)
b)
(2x+9)(2x-1)
c)
(4x-1)(x+9)
d)
(x+1)(4x-9)
7.
Factor:
 3x2-17x+10
a)
(x-5)(3x-2)
b)
(x+5)(3x+2)
c)
(3x-5)(x-2)
d)
(x+5)(3x-2)
8.

What are the solutions (5x - 1)(2x + 5)?

a)

1 and -5

b)

1/5 and -5/2

c)

5 and -2/5

d)

-1 and + 5

9.
Factor
9x2- 6x - 8
a)
(3x+2)(3x-4)
b)
(3x+2)(3x+4)
c)
(3x-2)(3x-4)
d)
(x-1)(9x+8)
10.
What are the solution(s)?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
11.
What are the factors AND solutions of
x2 + 2x – 3 = 0
a)
(x - 2)(x + 1); x=2, x=-1
b)
(x + 1)(x - 3); x=-1, x=3
c)
(x + 2)(x - 1); x=-2, x=1
d)
(x - 1)(x + 3); x=1, x=-3
12.
Solve:
 4x2 + 11x - 3 = 0
a)
x = -3/4 and x = -1
b)
x = 4 and x = 3
c)
x = 1/4 and x = -3
d)
x = -1/4 and x = 3
13.
a)
√3
b)
±√3
c)
-3
d)
No real solution
14.
a)
±81
b)
±9
c)
±3
d)
No real solution
15.
a)
± 1
b)
± 4/3
c)
± 3/4
d)
No real solution
16.
a)
-4, 2
b)
-2, 4
c)
-16
d)
-4
17.

Which expression represents the discriminant?

a)

aX2 + bX + c

b)

b - 4ac

c)

b2 - 4ac

d)

b2 + 4ac

18.

If the discriminant is zero, how many solutions will there be?

a)

no real solutions

b)

two real solutions

c)

1 real solution

19.

If the discriminant is positive, how many solutions will there be?

a)

one real solution

b)

two real solutions

c)

no real solutions

20.

If the discriminant is negative, how many solutions will there be?

a)

one real solution

b)

two real solutions

c)

no real solutions

21.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
22.
Which of the following equations matches standard form of a quadratic?
a)
ax + by = c
b)
y = a(x - h)2 + k
c)
y = ax2 + bx + c
d)
y = mx + b
23.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
24.
____________
For the function above, is the discriminant positive, negative, or zero?
a)
Positive
b)
Negative
c)
Zero
d)
Not Sure
25.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

one imaginary solution

26.
What do you do to the b value to correctly complete the square?
a)
square it
b)
divide it by 2 and square the result
c)
divide it by 2 and take the square root of the result
d)
divide it by 2 only
27.
What do you do to the b value to correctly complete the square?
a)
square it
b)
divide it by 2 and square the result
c)
divide it by 2 and take the square root of the result
d)
divide it by 2 only
28.
To solve by completing the square, what needs to be moved in this equation?
x2 = 9 - 4x
a)
the -4x
b)
the 9
c)
the x2
29.
What is the first step to solving THIS equation by completing the square?
a2 + 10a + 21 = 0
a)
Set the equation equal to zero
b)
Divide 10 by 2 and add the result to both sides
c)
Add a2 and 10a together
d)
Subtract the 21
30.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
31.
Complete the square.
x2 + 6x + ____
a)
x2 + 6x + 9
b)
x2 + 6x - 36
c)
x2 + 6x + 36
d)
x2 + 6x - 9
32.
Solve by completing the square.
y2 + 10y = -9
a)
1 and -12
b)
-1 and -9
c)
1 and -9
d)
1 and -1
33.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
34.
When do you use the plus or minus symbol?
±
a)
After taking the square root of both sides
b)
After adding the square to both sides
c)
After taking half of b
d)
After setting the equation equal to zero
35.
What is one of the solutions to this equation?
(2x - 1)2 = 49
a)
7
b)
-7
c)
-4
d)
-3
36.
Solve
4m2 - 100 = 0
a)
m=25, -25
b)
m=96
c)
m=5, -5
d)
m=-96
37.
Sammy is solving a quadratic equation by completing the square. She has gotten this far...
(x - 3)2 = 11
Which of the following equations is she trying to solve?
a)
x2 - 6x = 2
b)
x2 - 3x = 2
c)
x2 - 9x - 6 = 5
d)
x2 - 18x = -9x
38.
What are the solutions of x2 - 14x + 49 = 48?
a)
-7 ± 4√3
b)
-7 ± 16√3
c)
7 ± 4√3
d)
7± 16√3
39.
What are the solutions of x2 - 14x + 49 = 48?
a)
-7 ± 4√3
b)
-7 ± 16√3
c)
7 ± 4√3
d)
7± 16√3
40.
What do you do to the b value to correctly complete the square?
a)
square it
b)
divide it by 2 and square the result
c)
divide it by 2 and take the square root of the result
d)
divide it by 2 only
41.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
42.
Solve using the quadratic formula.
2x2-8x-24=0
a)
x= 6, -2
b)
x= 2, -6
c)
x= 4, 2
d)
x= 2, 6
43.
Solve using square roots.
k2 - 6 = 43
a)
k = √37
b)
k = 37 or - 37
c)
k = 7, k = -7
d)
no solution
44.
Solve using square roots.
5b2 - 4 = 41
a)
b = 9, b = -9
b)
b = 3, b = -3
c)
b = 8, b = -8
d)
no solution
45.
Solve
(x-5)2 = 25
a)
±0
b)
±10
c)
10, 0
d)
-10, 0
46.
Solve
(x+3)2-5 = 9
a)
±√14 -3
b)
√14 - 3
c)
±11
d)
±5
47.
Solve by completing the square.
x2 +12x = 5
a)
X = 6 + √41 or  6 − √41
b)
X= 35 or 47
c)
X = −6 + √41 or  −6 − √41
d)
X = √35 or √47
48.

What is the first step to solving THIS equation by completing the square?

a2 + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add the 21

d)

Subtract the 21

49.
Solve by completing the square. Round.
x2 -4x = 5
a)
11 and -7
b)
1 and 3
c)
1.73 and -1.73
d)
5 and -1
50.
Solve by completing the square. Round.
x2 -4x = 5
a)
11 and -7
b)
1 and 3
c)
1.73 and -1.73
d)
5 and -1
51.
Which is the best method to solve 4x2-12x=0
a)
Square roots
b)
Factoring
c)
Quadratic formula
d)
Completing Squares
52.
Which is the best method to solve 5x2-20=5?
a)
Square roots
b)
Factoring
c)
Quadratic Formula
d)
Completing squares
53.
Which is the best method to solve x2-6x+9=0?
a)
graphing
b)
square roots
c)
Quadratic formula
d)
completing squares or factoring
54.
Which is the best method for solving  3x2-4.5x-10.8=0 for an approximate answer.
a)
Square roots
b)
Graphing or quadratic formula
c)
Factoring 
d)
completing the square
55.
Which is the best method for solving      x2-4x +10=0 for exact answers?
a)
Square roots
b)
graphing
c)
Complete squares
d)
factoring
56.
Best method for solving
3(x-2)2-1=80  for exact answers?
a)
Square roots
b)
factoring 
factoring or completing squares
c)
graphing
d)
quadratic formula
57.
Best Method to solve  x2+10x=7 for exact answers?
a)
Square roots
b)
Graphing or factoring
c)
completing squares
d)
quadratic formula
58.
Best method for solving
 x2-2x-8=0?
a)
Square roots
b)
Factoring
c)
Quadratic formula
d)
Graphing 
59.
Best Method to solve  -2x2-6x-36=0?
a)
Square roots
b)
factoring
c)
quadratic formula 
d)
Completing the squares
60.
Solve by factoring:3x2 + 5x + 2 = 0  
a)
x = -2/3 and x = -1
b)
x = -3/2 and x = -1
c)
x = 2/3 and x = 1
d)
x = 2/3 and x = -1
61.
Solve by factoring:  4x2 + 11x - 3 = 0
a)
x = -3/4 and x = -1
b)
x = 4 and x = 3
c)
x = 1/4 and x = -3
d)
x = -1/4 and x = 3
62.
Factor: 49x2 - 100
a)
(49x + 100)(x - 1)
b)
(7x - 10)(7x + 10)
c)
(49x - 10)(x + 10)
d)
(7x -10)(7x - 10)
63.
Solve for x.
6x2 - 9 = 87
a)
x = 4, -4
b)
x = 4
c)
x = 16
d)
x = 16, -16
64.
5(x-8)2=15
a)
{√3,-√3}
b)
{8+√3,8-√3}
c)
{2√2,-2√2}
d)
no solution
65.
Solve by taking square roots:
(2x+6)2 + 8 = 24
a)
x = - 1 , x = - 5 
b)
x = - 1 , x = 5 
c)
x = 1 , x = 5
d)
x = 1 , x = - 5
66.
The quadratic equation can be used to solve quadratic equations that cannot be factored.
a)
True
b)
False
67.

The discriminant is

a)

ax2 + bx + c

b)

b - 4ac

c)

b2 - 4ac

d)

b2 + 4ac

68.
Solve using the quadratic formula. 
12x + 9x2 = 5
a)
x = -6/18 and 30/18
b)
x = -5/3 and 1/3
c)
x = 5/3 and -1/3
d)
x = 6/18 and -30/18
69.
Determine the # of real solutions. 
x + 2 = -3x2
a)
One
b)
Two
c)
Zero
d)
Infinite
70.
Determine the # of real solutions. 
4x2 - 2x = 10
a)
Zero
b)
One
c)
Two
d)
Three
71.
Solve using square roots.      3x2 - 15 = 0
a)
x = -√5
b)
x = 5 and -5
c)
x = √5
d)
x = √5 and -√5
72.
Solve by completing the square. x2 - 2x = 5
a)
x = 1 ± √6
b)
x = 3 and -1
c)
x = -1 ± √6
d)
x = 1 and -3
73.
Solve the equation by factoring:
x2 -5x = 24
a)
x = ±√5
b)
x = -8 and 3
c)
x = 8 and -3
d)
No Real Solution
74.
Solve using the quadratic formula. 
x2 + 10x = -25
a)
x = -5
b)
x = ±5
c)
x = 5
d)
x = 0
75.
Solve by completing the square. 
3x2 - 12x + 6 = 0
a)
x = 2 ± √-6
b)
x = 2 ± √6
c)
x = -2 ± √2
d)
x = 2± √2
76.
Determine the # of real solutions. 
12x2 + 12x = -3
a)
0
b)
1
c)
2
d)
4
77.

Find the value of c that completes the square. a2 – 6a + c

a)

81

b)

36

c)

9

d)

9/4

78.

Find the value that completes the square then rewrite as a perfect square. x2 – 8x + ___

a)

16; (x – 8)2

b)

196; (x – 14)2

c)

–4; (x – 4)2

d)

16; (x – 4)2

79.

For the next few problems, you will answers questions relating to solving the following by COMPLETING THE SQUARE.

p2 + 16p + ___ = 36


What does b/2 = ?

a)

16

b)

8

c)

18

d)

4

80.

For the next few problems, you will answers questions relating to solving the following by COMPLETING THE SQUARE.

p2 + 16p + 64 = 36 + 64


b/2 = 8, c = 64

Write this as a perfect square.

a)

(p + 16)2 = 100

b)

(p + 64)2 = 100

c)

(p + 4)2 = 100

d)

(p + 8)2 = 100

81.

For the next few problems, you will answers questions relating to solving the following by COMPLETING THE SQUARE.

6k2 – 12k + ___ = 48


What are you left with after you divide out your a value?

a)

6(k2 – 6k + ___) = 48

b)

6(k2 – 12k + ___) = 48

c)

6(k2 – 2k + ___) = 48

82.

For the next few problems, you will answers questions relating to solving the following by COMPLETING THE SQUARE.

p2 + 16p + 64 = 36 + 64

(p + 8)2 = 100

Finish solving the problem.

a)

p = 2, p = –18

b)

p = 10, p = –10

c)

p = –2, p = 18

d)

p = 8, p = –2

83.

For the next few problems, you will answers questions relating to solving the following by COMPLETING THE SQUARE.

6k2 – 12k + ___ = 48

6(k2 – 2k + ___) = 48


What does b/2 = ? *use the 2nd expression*

a)

–1

b)

–2

c)

–6

d)

–12

84.

Write the following as a perfect square.

Use COMPLETING THE SQUARE.

5v2 – 20v + ____ = 25

*make sure you balance the right side of the equation*

a)

5(v – 2)2 = 45

b)

5(v – 2)2 = 25

c)

5(v – 4)2 = 45

d)

5(v – 4)2 = 30

85.

Find the discriminant of each quadratic equation then state the number and type of solutions.

9v2 – 6v + 15 = 5

a)

–324; two imaginary solutions

b)

316; two real solutions

c)

161; two real solutions

d)

–324; two real solutions

86.

Convert to standard form (multiply out completely)

y = 3(x – 2)2 + 17

a)

y = 9x2 –12x + 53

b)

y = x2 – 4x + 4

c)

y = 3x2 – 12x + 29

d)

y = 3x2 –12x + 21

87.
What is the vertex?
a)
(0, - 1)
b)
(0, 0.5)
c)
(-1, 0)
d)
(0.5, 0)
88.
b2  would equal: y = 2x2 -x -3
a)
2
b)
-1
c)
1
d)
-3
89.
4ac would equal:  y = 2x2 -x -3
a)
-12
b)
8
c)
-24
d)
-1
90.
True or false:
The solution, root, x-intercept, and zero of a problem are all the same thing
a)
True
b)
False, because the solution and root are the same but the x-intercept and zero are different
c)
False, because the x-intercept and root are the same but the zero and solution are different
d)
False, they are all different
91.
Solve using the quadratic formula.
2x2 - 9x - 35 = 0
a)
x = 7/2, x = -6
b)
x = -5/2, x =5
c)
x = -3/7, x =6
d)
x = -5/2, x = 7
92.
a)
A
b)
B
c)
C
d)
D
93.
In the expression 4x2-5x+9 the leading coefficient is
a)
9
b)
-5
c)
-4
d)
4
94.
The solution of the quadratic equation
4x2-5x-9=0 are
a)
x=-1 or x=9/4
b)
x=1 or x=9/4
c)
x=2 or x=3
d)
x=-2 or x=-3
95.
Fill the blank space to complete the perfect square trinomial
x2-18x+____=(x- ____)2
a)
9 and 3 respectively
b)
81 and 9 respectively
c)
-9 and -3 respectively
d)
-81 and -9 respectively

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