Free Printable Unit 1 Review: Quadratics

1.

The imaginary number i is equal to...

a)

i

b)

1

c)

-i

d)

-1

2.

The imaginary number $i^2$ is equal to...

a)

i

b)

1

c)

-i

d)

-1

3.

The imaginary number $i^3$ is equal to...

a)

i

b)

1

c)

-i

d)

-1

4.

The imaginary number $i^4$ is equal to...

a)

i

b)

1

c)

-i

d)

-1

5.

The discriminant is which choice?

a)

$b^2-4ac$

b)

$a^2+b^2=c^2$

c)

$y=mx+b$

d)

$y=ax^2+bx^2+c$

6.

Factor completely: $8x^2+12x$

a)

$4x\left(2x+3\right)$

b)

$4x\left(2x-3\right)$

c)

$4\left(2x+3\right)$

d)

$4\left(2x^2+3x\right)$

7.

Factor completely: $x^2+5x-6$

a)

$\left(x-1\right)\left(x-6\right)$

b)

$\left(x+1\right)\left(x+6\right)$

c)

$\left(x+6\right)\left(x-1\right)$

d)

$\left(x-1\right)\left(x+6\right)$

8.

Which term is associated with the AC Method?

a)

factor by grouping

b)

the quadratic formula

c)

the pythagorean theorem

d)

the squeeze theorem

9.

The factors $\left(x+2\right)$ and $\left(x-2\right)$ are _______?

a)

conjugate pairs

b)

circles

c)

squares

d)

invisible

10.

The roots of the given equation, $\left(x+2\right)\left(2x-9\right)=0$ , are...?

a)

$x=-2,\ x=\frac{9}{2}$

b)

$x=-2,\ x=\frac{2}{9}$

c)

$x=2,\ x=\frac{9}{2}$

d)

$x=2,\ x=\frac{2}{9}$

11.

State the maximum number of unique zeros any given quadratic equation can have.

a)

zero

b)

one

c)

two

d)

three

12.

The form, $y=ax^2+bx+c$ , is the ______ form of a quadratic equation.

a)

standard

b)

pythagorean theorem

c)

linear

d)

slope

13.

TRUE OR FALSE: The signs of the coefficients in a quadratic equation / expression helps us determine the signs of its factors.

a)

TRUE

b)

FALSE

14.

The expression $x^2-10x+24$ is equivalent to...?

a)

$\left(x+12\right)\left(x-2\right)$

b)

$\left(x-12\right)\left(x+2\right)$

c)

$\left(x+6\right)\left(x+4\right)$

d)

$\left(x-6\right)\left(x-4\right)$

15.

Daniel correctly factored the expression $m^2-12m-64$ . Which expression did he write?

a)

$\left(m-8\right)\left(m-8\right)$

b)

$\left(m-8\right)\left(m+8\right)$

c)

$\left(m-16\right)\left(m+4\right)$

d)

$\left(m+16\right)\left(m-4\right)$

16.

When the discriminant is greater than 0, it has ____ x-intercepts.

a)

0

b)

1

c)

2

d)

3

17.

When the discriminant is equal to 0, it has ____ x-intercepts.

a)

0

b)

1

c)

2

d)

3

18.

When the discriminant is less than 0, it has ____ x-intercepts.

a)

0

b)

1

c)

2

d)

3

19.

If $b^2-4ac<0$ , then its roots are...?

a)

imaginary

b)

real, rational, equal

c)

real, rational, unequal

d)

real, irrational, unequal

20.

If $b^2-4ac=0$ , then its roots are...?

a)

imaginary

b)

real, rational, equal

c)

real, rational, unequal

d)

real, irrational, unequal

21.

If $b^2-4ac>0$ and is a nonperfect square, then its roots are...?

a)

imaginary

b)

real, rational, equal

c)

real, rational, unequal

d)

real, irrational, unequal

22.

If $b^2-4ac>0$ and is a perfect square, then its roots are...?

a)

imaginary

b)

real, rational, equal

c)

real, rational, unequal

d)

real, irrational, unequal

23.

The roots of the equation $9x^2+3x-4=0$ are...?

a)

imaginary

b)

real, rational, and equal

c)

real, rational, and unequal

d)

real, irrational, and unequal

24.

The roots of the equation $x^2-10x+25=0$ are...?

a)

imaginary

b)

real, rational, and equal

c)

real, rational, and unequal

d)

real, irrational, and unequal

25.

Which graph represents a quadratic function with a negative discriminant?

a)

b)

c)

d)

26.

Which if the following is an equation for a quadratic function that opens downward (concave down) and has the vertex of (-4, 7)?

a)

$f\left(x\right)=-\left(x-4\right)^2+7$

b)

$f\left(x\right)=\left(x+4\right)^2+7$

c)

$f\left(x\right)=-\left(x+4\right)^2+7$

d)

$f\left(x\right)=\left(x-4\right)^2+7$

27.

How does the graph of $g\left(x\right)=3x^2$ compare to the quadratic parent function $f\left(x\right)=x^2$ ?

a)

The graph of g(x) is wider than the graph of f(x).

b)

The graph of g(x) is narrower than the graph of f(x).

c)

The graph of g(x) is translated up 3 units above f(x).

d)

The graph of g(x) is translated down 3 units below f(x).

28.

How would you describe the translation from f(x) = x² to g(x) = (x - 3)² ?

a)

Horizontal translation: three units to the left

b)

Horizontal translation: three units to the right

c)

Vertical translation: three units up

d)

Vertical translation: three units down

29.

Which describes the transformation of the graph of f(x) = x² to the graph of g(x) = -4x²

a)

Reflected, narrower

b)

reflected, wider

c)

shifted down 4 units

d)

shifted up 4 units

30.

Which quadratic is the narrowest graph?

a)

y = 3x²

b)

y = 4x²

c)

y = 2x²

31.

Which quadratic graph is the widest?

a)

y = 5x²

b)

y = -¼x²

c)

y = -½x²

d)

y = 5x²

32.

If the blue graph is
f(x) = x²
then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

33.

What are the zeros for the quadratic function?

a)

(-6, 0) and (14, 0)

b)

(-50, 0) and (14, 0)

c)

(-6, 0) and (-50, 0)

d)

(-50, 0) and (-60, 0)

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.

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

36.

If the graph of a quadratic does not intercept the x-axis at any point, then it has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

37.

What does the discriminant tell us?

a)

The maximum or minimum

b)

The y-intercept

c)

The number and type of solutions

d)

The axis of symmetry

38.

What are the solutions to x² - 3x = 5?

a)

b)

c)

d)

39.

____________
For the function above, is the discriminant positive, negative, or zero?

a)

Positive

b)

Negative

c)

Zero

d)

Not Sure

40.

Simplify the given expression: $\left(2x-3\right)\left(x+4\right)$

a)

$2x^2+8x-3x-12$

b)

$2x^2-12$

c)

$2x^2+5x-12$

d)

$2x^2-5x-12$

41.

Simplify the given expression: $\left(y-6\right)\left(y-4\right)$

a)

$y^2-10y+24$

b)

$y^2-4y-6y+24$

c)

$y^2+24$

d)

$y^2-24$

42.

Find the GCF of 3r and 18

(a)

43.

The GCF of 7r² and 49r is.....

a)

7

b)

7r

c)

49r

d)

49

44.

Identify the a, b, and c values for this quadratic:

6x+3x^2-7

a)

a= 3 b=6 c=7

b)

a=6 b=3 c=7

c)

a=3 b=6 c=-7

d)

a=6 b=3 c=-7

45.

Simplify the given expression: (2+ 5i) + (3 - 8i)

a)

1 - 3i

b)

1 - 13i

c)

5 - 3i

d)

5 + 13i

46.

Simplify the given expression: ( 5 + i ) - ( 2i - 3 )

a)

3i - 2

b)

8 - i

c)

8 + i

d)

3i + 2

47.

Simplify the given expression: ( 3 + 2i ) - ( 7 + 7i )

a)

-4 + 5i

b)

4 + 5i

c)

4 - 5i

d)

-4 - 5i

48.

Write the equation in vertex form. $y\ =\ x^2+\ 2x\ +\ 5\$

a)

$y=\left(x+1\right)^2\ -\ 4\$

b)

$y=\left(x+1\right)^2\ +4$

c)

$y=\left(x-4\right)^2-1$

d)

$y=\left(x+4\right)^2+1$

49.

What is the vertex of the given equation? $y=\left(x+1\right)^2+4$

a)

(1,4)

b)

(-1,-4)

c)

(-1,4)

d)

(1,-4)

50.

Does this equation have a maximum or a minimum?

y=-\left(x+1\right)^2+4

a)

Max is -1

b)

Min is -1

c)

Max is 4

d)

Min is 4

51.

Does this equation have a maximum or a minimum? $y=\left(x-5\right)^2$

a)

Max is -5

b)

Min is -5

c)

Max is 0

d)

Min is 0

52.

Solve the following quadratic linear system

y=x^2+2x\ +\ 6

,

y=-x\ +4

a)

(1,5) and (2,6)

b)

(-1,5) and (2,6)

c)

(-1,5) and (-2,6)

d)

(-1,5) and (2,6)

53.

$\sqrt{50x^3y}$ Simplify

a)

$5\sqrt{2xy}$

b)

$5x\sqrt{2xy}$

c)

$5ix\sqrt{2xy}$

d)

$5x^2\sqrt{2xy}$

54.

$\sqrt{-48x^{10}y^5}$ Simplify

a)

$4ix^{10}y^2\sqrt{3y}$

b)

$16ix^5y^4\sqrt{3y}$

c)

$4ix^5y^2\sqrt{3y}$

d)

$16x^5y^2\sqrt{3y}$

55.

Which of the following symbols read as greater than?

a)

$>$

b)

$<$

c)

$\ge$

d)

$\le$

56.

Which of the following symbolizes less than?

a)

$>$

b)

$<$

c)

$\le$

d)

$\ge$

57.

Which inequality is shown?

a)

y < -x²

b)

y ≤ -x²

c)

y > -x²

d)

y ≥ -x²

58.

Solve the given inequality: 2x² + 5x ≥ 12

a)

$-4\le x\le1.5$

b)

$x<-4\ \ or\ \ x>1.5$

c)

$x\le-4\ \ or\ \ x\ge1.5$

d)

no solution

59.

Which inequality is represented by the graph?

a)

y > (x - 3)² - 3

b)

y ≥ (x + 3)² - 3

c)

y > (x + 3)² - 3

d)

y ≥ (x - 3)² - 3

60.

a)

y ≥ -(x + 4)² + 1

b)

y < -(x - 4)² + 1

c)

y ≤ (x - 4)² + 1

d)

y ≤ -(x - 4)² + 1

61.

Which inequality is represented by the graph?

a)

y > -(x - 4)² + 1

b)

y > -(x - 1)² + 4

c)

y < (x - 4)² + 1

d)

y > (x + 4)² + 1

62.

a)

y ≤ (x - 3)² + 3

b)

y < (x + 3)² - 3

c)

y < (x - 3)² - 3

d)

y ≤ (x + 3)² - 3

63.

Solutions are in the ___________ area.

a)

non-shaded

b)

shaded

c)

vertex

d)

axis of symmetry

64.

Simplify the given expression.

a)

10

b)

-10

c)

10i

d)

-10i

65.

Simplify the given expression.

a)

5i

b)

-5i

c)

5+i

d)

-5

66.

What is the complex conjugate of 4 - 3i?

a)

$\frac{1}{4-3i}$

b)

$\frac{1}{4+3i}$

c)

-4 + 3i

d)

4 + 3i

67.

Simplify the given expression:

(7 + 2i)(9 - 6i)

a)

75-24i

b)

63 - 24i - 12i²

c)

51 - 24i

d)

58 + 60i

68.

Simplify the given expression: $\sqrt{-25}$

a)

-5i

b)

5

c)

5i

d)

-5

69.

Factor completely: $x^2-1$

a)

(x+1)(x +1)

b)

(x - 1)(x - 1)

c)

prime

d)

(x + 1)(x - 1)

70.

Factor completely: x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

71.

Factor completely: 4x² - 25

a)

(2x + 5) (2x - 5)

b)

(2x - 5)²

c)

(2x + 5)²

d)

2x + 5(2x - 5)

72.

Factor completely: x² - 16

a)

(x + 4) (x - 4)

b)

(x + 8) (x - 2)

c)

(x + 4)²

d)

x + 4(x - 4)

73.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

74.

What are the solutions to the graphed system?

a)

(0,-2) and (3,1)

b)

(-2,0) and (2,0)

c)

(0,-2) and (3,1)

d)

(2,2) and (1,0)

75.

Solve the system of linear and quadratic equations:

y = 5

y = 2x² - 16x + 29

a)

(6, 5) and (2, 5)

b)

(2, 6)

c)

(6, 2)

d)

(5, 6) and (5, 2)

76.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

77.

What is the solution to the linear-quadratic system graphed in the picture.

a)

(0, 0)

b)

(3, 0)

c)

(2, -3)

d)

(-3, 2)

78.

Find the solution.

a)

(4,2) and (0,9)

b)

(-4,-1) and (2,5)

c)

(5,3) and (5,2)

d)

(-4,2) and (5,9)

79.

Find the solution.

a)

(6,4) and (3,1)

b)

(-2,7) and (5,2)

c)

(5,4) and(-2,-5)

d)

(1,-1) and (4,2)

80.

Which of the following represents "a number greater than 3"?

a)

x < 3

b)

x > 3

c)

x ≥ 3

d)

x ≤ 3

81.

Which of the following represents "a number less than 0"?

a)

x < 0

b)

x ≥ 0

c)

x ≥ 0

d)

x > 0

82.

Which inequality matches this situation:
You must be at least 18 years old to vote

a)

x > 18

b)

x < 18

c)

x ≤ 18

d)

x ≥ 18

83.

Which of the following represents "a number less than or equal to -5"

a)

x < -5

b)

x ≥ -5

c)

x > -5

d)

x ≤ -5

84.

Match:
You must be at least 48 inches tall to ride the bumper cars.

a)

h < 48

b)

h > 48

c)

h ≤ 48

d)

h ≥ 48

85.

When graphing b< 6 would you use an open or closed circle?

a)

Open

b)

closed

86.

Will my circle be colored in?
5 ≥ x

a)

Yes

b)

No

87.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

88.

Pick the correct inequality.

a)

A

b)

B

c)

C

d)

D

89.

What type of circle will be used?
5 ≥ x

a)

Open

b)

Closed

90.

What inequality does the number line graph represent?

a)

-5 ≥ x

b)

x < −5

c)

x > -5

d)

x ≥ −5

91.

Which graph matches the inequality
r ≥ -6?

a)

A

b)

B

c)

C

d)

D

92.

Does this parabola have a maximum or minimum?
REMEMBER MAXIMUM IS THE HIGHEST AND MINIMUM IS THE LOWEST.

a)

Maximum

b)

Minimum

93.

If the a value is positive, which direction does the graph open?

a)

up

b)

down

c)

left

d)

right

94.

If the a value is negative, which direction does the parabola open?

a)

up

b)

down

c)

left

d)

right

95.

Does this graph have a maximum or minimum?

a)

Minimum

b)

Maximum

96.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

97.

Is this a max or min?

a)

max

b)

min

c)

cannot be determined

98.

The highest or lowest point on a quadratic is called the...

a)

Max

b)

Vertex

c)

Axis of Symmetry

d)

Intercept

99.

The line that goes through the vertex of a parabola is called the...

a)

Vertex

b)

Axis of Symmetry

c)

x-intercept

d)

y-intercept

100.

This graph is...

a)

Concave up

b)

Concave down

101.

If a quadratic has a vertex that is a maximum, then the quadratic is...

a)

Concave up

b)

Concave down

102.

How many x-intercepts does this quadratic have?

a)

0

b)

1

c)

2

d)

infinitely many

103.

If a quadratic is concave up, then the vertex is the...

a)

Minimum point

b)

Maximum point

104.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

y intercept

105.

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

a)

a reflection across the line x = -4

b)

a reflection across the line y = -4

c)

a translation shifting f(x) 4 units to the left

d)

a translation shifting f(x) 4 units to the right

106.

Pablo throws a ball with a path of
h = -5(t - 2)².
Maria throws a ball with a path of
h = -5(t - 2)² + 10.
Which description is reasonable for the difference in the two equations?

a)

Maria throws the ball 10 times harder than Pablo does.

b)

Maria starts her ball at a height 10 feet higher than Pablo does.

c)

Pablo throws the ball 10 times harder than Maria does.

d)

Pablo starts his ball at a height 10 feet higher than Maria does.

107.

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

a)

Nothing happens, it stays the same.

b)

Vertical stretch by a factor of 2.

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

108.

Which transformation will occur if f(x) = x² is replaced with -f(x)?

a)

Nothing happens, it stays the same.

b)

Vertical stretch by a factor of 2.

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

109.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

110.

What steps transform the graph y = x² to y = x² + 8

a)

shifted up 8 units

b)

shifted down 8 units

c)

shifted left 8 units

d)

shifted right 8 units

Unit 1 Review: Quadratics

Total questions: 110

Worksheet time: 3hrs 42mins

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