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Algebra Quarter 3 Topics

Total questions: 95

Worksheet time: 6hrs 13mins

Name
Class
Date
1.
Simplify:
a)
√12
b)
(4√3)/3
c)
√3
d)
(2√3)/3
2.
Simplify:
a)
√4√12
b)
4√12
c)
4√3
d)
2√3
3.
Simplify:
a)
5x√2
b)
100x√2
c)
10x√2
d)
10√2x
4.
Simplify:
a)
A
b)
B
c)
C
d)
D
5.
√5 × √10
a)
50
b)
2√5
c)
5√2
d)
5√10
6.
a)
11√5
b)
11√10
c)
5√5
d)
12√10
7.
a)
17√2
b)
9√1
c)
9
d)
9√2
8.
a)
13√3
b)
10√30
c)
13√6
d)
11√3
9.

Factor 4x + 6

a)

4(x + 2)

b)

2(2x + 3)

c)

2(2x + 4)

d)

4(x + 2/3)

10.

Find the factors of

x2 + x - 6

a)

(x - 6)(x - 9)

b)

(x + 3)(x + 2)

c)

(x + 3)(x - 2)

d)

(x + 2)(x + 4)

11.

Find the factors of

x2 - 5x - 36

a)

(x + 4)(x - 9)

b)

(x - 4)(x + 9)

c)

(x - 9)(x + 6)

d)

(x + 4)(x + 9)

12.

Find the factors of

5m2 - 45m + 90

a)

3(m + 1)(m + 8)

b)

5(m - 3)(m - 6)

c)

2(m - 7)(m + 3)

d)

5(m - 5)(m + 3)

13.

Find the factors of

2x2 + 21x + 10

a)

(2x + 1)(x + 10)

b)

(3x + 10)(x - 6)

c)

2(x + 1)(x + 5)

d)

2(x + 1)(x - 10)

14.

Find the factors of

5n2 + 11n - 12

a)

(n - 4)(5n + 3)

b)

(5n - 4)(n + 3)

c)

(2n - 9)(n - 8)

d)

(3n + 10)(n + 10)

15.
What is the axis of symmetry?
f(x) = x2 - 8x + 15.
a)
x = -4
b)
x = 4
c)
y = 4
d)
y = -4
16.
What is the y-intercept?
f(x) = -2x2 + 4x - 6
a)
(0, 6)
b)
(0, -6)
c)
(6, 0)
d)
(-6, 0)
17.
What do we call the highest or lowest point of a quadratic?
a)
parabola
b)
vertex
c)
graph
d)
point
18.
What is the vertex?
f(x) = -x2 - 4x + 12.
a)
(-2, 16)
b)
(2, 0)
c)
(2, 4)
d)
(-2, 4)
19.
What is the green dot on the parabola called?
a)
maximum
b)
minumum
c)
roots
d)
zeros
20.
.How many zeros does this parabola have? 
a)
3
b)
2
c)
0
d)
1
21.

The standard form of a quadratic function is

a)

ax2 + bx + c

b)

a(x - h)2 + k

c)

y - y1 = m(x - x1)

d)

Ax + By = C

22.

Identify A, B, and C if y=3x2-8+5x

a)

A=3, B=5, C=-8

b)

A=3, B=-8, C=5

c)

A=3x2, B=5x, C=-8

d)

A=3x2 , B=-8, C=5x

23.
What is c in the following equation?
y=ax2+bx+c
a)
Zeroes
b)
Axis of Symmetry
c)
Direction
d)
y-intercept
24.

What is the formula to find the axis of symmetry of a parabola?

a)

x = -b/2

b)

x = -b

c)

x = -b / (2a)

d)

x = -b / 2

25.

Comparing the functions, which is the most narrow?

a)

f(x)=3x2

b)

g(x)= -2x2

c)

h(x)=0.5x2

d)

a(x)=12x2

26.

Changing the c value of a standard form quadratic (y=ax2+bx+c) transforms the graph how?

a)

Up or down

b)

Left or right

c)

Reflects over x axis

d)

Up only

e)

Creates a change in the universe that is so chaotic it creates a new galaxy

27.

 f(x)=−x2−4f\left(x\right)=-x^2-4  

Which equation is the result of shifting this function down 3 units ?

a)

g(x)= - x2-1

b)

g(x)= - 4x2-4

c)

g(x) = -1/3x2-4

d)

g(x)= - x2-7

28.

Which of the following is true when the graph of f(x)=x2+4 is transformed into the graph g(x)=2x2+4

a)

The new function has more zeroes than the old function

b)

Both functions have the same vertex

c)

The function is translated up

d)

The axis of symmetry changes

29.

Comparing to f(x)=x2, select all of the transformations of g(x)=-5x2+11

a)

Reflected over x axis

b)

Vertical stretch by 5

c)

Vertical stretch by 11

d)

Up 11

e)

Left 11

30.

What are the x-intercepts of the parabola?

y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5,0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

31.

Which of the following is the Factored Form of a quadratic function?

a)

f(x) = mx + b

b)

f(x) = ax2 + bx + c

c)

f(x) = a(x - m)(x - n)

d)

f(x) = a(x - h)2 + k

32.
What is the green dashed line called?
a)
roots or x-intercepts
b)
parabola
c)
axis of symmetry
d)
line of dashes
33.

A parabola has a vertex at (-3,2).

Where is the axis of symmetry?

a)

y = 2

b)

x = 2

c)

x = -3

d)

y = -3

34.
Identify the vertex and whether the graph opens up or down.
a)
(5, 2); opens up
b)
(5, 2); opens down
c)
(-5, 2); opens up
d)
(-5, 2); opens down
35.

Given the equation for this parabola:

y= - (x-4)2 - 3,

does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

c)

Not enough information

36.
Which equation has a vertex of (-3, 4)?
a)
y = 2(x+3)2 + 4
b)
y = (x+3)2 - 4
c)
y = (x-3)2 + 4
d)
y = 2(x - 3)2 + 4
37.
What is the domain of the function y = x2 + 3?
a)
All Real Numbers
b)
x>3
c)
x<3
d)
It is impossible to determine.
38.
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
39.

What is the range of the function?

a)

All Real Numbers

b)

y≤0y\le0

c)

y≥4y\ge4

d)

y≤4y\le4

40.

If a parabola opens downward and has x-intercepts at (0, 5) and (0, 6), what is the equation?

a)

y = a(x + 5)(x + 6), a < 0

b)

y = a(x - 5)(x - 6), a < 0

c)

y = a(x + 5)(x + 6), a > 0

d)

y = a(x - 5)(x - 6), a > 0

41.
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
42.
What is the range of this function?
a)
All real numbers.
b)
All real numbers greater than or equal to 0.
c)
All real numbers greater than or equal to -2.
d)
All real numbers greater than or equal to 2.
43.
When factoring
x2 - 4x + 4 = 20,
what goes in the blank?
(x - __ )2 = 20
a)
4
b)
2
c)
8
d)
20
44.
Complete the square.
x2 + 6x + ____
a)
x2 + 6x + 9
b)
x2 + 6x - 36
c)
x2 + 6x + 36
d)
x2 + 6x - 9
45.
Complete the square.
x2 + 14x + ____
a)
x2 + 14x - 196
b)
x2 + 14x + 49
c)
x2 + 14x - 49
d)
x2 + 14x + 196
46.
Solve by completing the square.
y2 + 10y = -9
a)
1 and -12
b)
-1 and -9
c)
1 and -9
d)
1 and -1
47.

Write the following quadratic expression in vertex form...


x2 + 4x + 10

a)

(x + 4)2 + 6

b)

(x + 2)2 + 6

c)

(x + 4)2 - 6

d)

(x + 2)2 - 6

48.
What are the zeros?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
49.
Convert x2-6x+9 to factored form and identify the solution.
a)
(x-3)(x-3); x=3
b)
(x+3)(x+3); x=-3
c)
(x+4)(x+2); x=-4, -2
d)
Not factorable
50.
a)
±81
b)
±9
c)
±3
d)
No real solution
51.
y=2x2-6x+1 is in what form?
a)
Vertex Form
b)
Factored form
c)
Standard Form 
d)
Cannot be determined
52.

What is the domain of

f(x) = x² - 4 ?

a)

x = all real numbers

b)

x ≥ - 4

c)

y ≤ 0

d)

y ≥ - 4

53.
What is the GCF of 18k and 15k3
a)
3k2
b)
3k3
c)
3k
d)
5k
54.

Factor completely

10x2 + 15x - 5

a)

25 (10x3 + 45x - 15)

b)

5 (2x3 + 3x2 - x)

c)

x (10x3 + 15x - 5)

d)

5 (2x2 + 3x - 1)

55.
Find the product.
(x + 7)2
a)
x2 + 7x + 7x + 49
b)
x2 + 7x + 7
c)
7x2 + x + 7
d)
x2 + 14x + 49
56.

Solve

n4 - 49n2 = 0

a)

0, 7

b)

0, -7, 7

c)

0, -7

d)

7, -7

57.
x2 + 81
a)
Prime
b)
( x - 9 ) ( x + 9 ) 
c)
( x + 9 ) ( x + 9 ) 
d)
( x - 9 ) ( x - 9 ) 
58.
x2 - 16
a)
Prime
b)
( x - 4) ( x + 4) 
c)
( x - 8) ( x + 8) 
d)
( x - 4) ( x - 4) 
59.
w3 + 3w
a)
3w(1)
b)
w(w2 + 3)
c)
w3(w + 3)
60.

Factor completely:

3x2 + 18x +15

a)

3(x2 + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

61.

Factor the polynomial.

x2 - 4x - 32

a)

(x-8)(x+4)

b)

(x-4)(x-32)

c)

(x+3)(x-4)

d)

(x+2)(x+5)

62.
Factor
x2 - 13x + 36
a)
A
(x + 9)(x + 4)
b)
B
(x - 9)(x - 4)
c)
C
(x + 9)(x - 4)
d)
D
(x - 9)(x + 4)
63.
Factor
3v2 - 4v - 7
a)
(3v-7)(v+1)
b)
3(v-7)(v-1)
c)
(3v+1)(v-9)
d)
(3v+1)(v-10)
64.
Factor:
x2 - 49
a)
(x + 7)(x - 7)
b)
(x + 7)2
c)
(x - 7)2
d)
(x+7)(x-1)
65.
Factor by grouping
x3 - 4x2 -4x + 16
a)
(x+4)(x+2)
b)
(x-4)(x2 -4) 
c)
(x+4)(x2 -4)
d)
(x-4)(x-2)
66.
Which is a zero of the graph?
a)
0
b)
-1
c)
1.5
d)
-3
67.
What are the roots of the function
f(x)= (x - 2)(x + 3)?
a)
x = - 2 or x = 3
b)
x = 2 or x = -3
c)
The are no real roots
d)
x = 2 or x = 3
68.
Which of the following is a solution to the function?  (x - 8)(x - 9) = 0
a)
8
b)
-9
c)
-17
d)
0
69.
What are the zeros of the quadratic function?
y = x2 - 2x - 15
a)
x = -2
x = -15
b)
x = -3
x = 5
c)
x = 3
x = -5
d)
x = 1
x = -16
70.
What are the green dots called?
a)
axis of symmetry
b)
vertex
c)
parabola
d)
roots or x-intercepts
71.
What is the equation for axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
72.
Find the y-intercept of f(x) = 2x2 - 2x + 1
a)
2
b)
-2
c)
1
d)
-1
73.

The U-Shaped curve of a quadratic equations is called a ______

a)

parabola

b)

maximum

c)

minimum

d)

bolapara

74.

A positive parabola opens ___

a)

up

b)

down

c)

sideways

d)

seriously?

75.

The formula to find the Axis of Symmetry :

a)
b)
c)
76.

A parabola has a vertex at (-3,2).

Where is the axis of symmetry?

a)

y = -2

b)

x = 2

c)

x = -3

d)

y = -3

77.

Find the Vertex: y= x2 +6x + 4

a)

(-3, -5)

b)

(5, 3)

c)

(3, 5)

d)

(5, -3)

78.
Does this graph have a maximum or a minimum?
a)
Maximum
b)
Minimum
79.
What is the range of this quadratic graph?
a)
y ≥ 3
b)
y ≤ 3
c)
ℝ
d)
y ≤ 2
80.

How many zeros does this quadratic function have ?

a)

no solutions

b)

2

c)

1

d)

infinitely many

81.
How many solutions does this graph have?
a)
one
b)
two
c)
no solutions
d)
cannot be determined
82.
Which point is an example of a y-intercept?
a)
(3,4)
b)
(-2,8)
c)
(0,4)
d)
(5,0)
83.

Simplify completely.

a)

8√3xy

b)

y√24xy

c)

8y√3xy

d)

8√24x

84.
In the quadratic formula, if b2-4ac>0, then the quadratic equation has
a)
two imaginary solutions
b)
two different real solutions
c)
two equal real solutions
d)
none of these
85.
In the quadratic formula, the expression
b2-4ac is called
a)
discrim
b)
determinant
c)
discriminant
d)
none of these
86.
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
87.
One solution of the quadratic equation
x2-7x+12=0 is
a)
x=3
b)
x=2
c)
x=-3
d)
x=-2
88.

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

89.

What is this formula?

a)

This is the standard formula.

b)

This is the quadratic formula.

c)

This is the factored formula.

d)

This is the vertex formula.

90.

Solve 2x2 + 7x - 15 = 0

a)

-3/2 or 5

b)

No Solution

c)

-5 or 3/2

d)

0.7 or 5

91.
a)
A
b)
B
c)
C
d)
D
92.

Solve using the Quadratic Formula


4v2 - 1v - 18 = 0

a)

v = 2.25, -2

b)

v = -2.25, 2

c)

v = 2.24, -1.99

d)

v = -2.24, 1.99

93.
Solve     8x2 - 6x + 1 = 0
a)
No Solution
b)
0 or 1
c)
-0.5 or -0.25
d)
0.25 or 0.5
94.
a)

0

b)

± 5\pm\ 5

c)

no solution

d)

± 25\pm\ 25

95.

If the discriminant equals 0, then the quadratic has:

a)

1 Rational Solution

b)

2 Rational Solutions

c)

No solutions

d)

2 Complex Solutions

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