Free Printable Ch. 9 Quadratic Equations

1.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

2.

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

Where is the axis of symmetry?

a)

y = -2

b)

y = 3

c)

x = -3

d)

x = 2

3.

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

4.

What is the vertex?

a)

(4,-4)

b)

(2,0)

c)

(0,2)

d)

(6,0)

5.

What is a, b, and c in 3x² + 4 = 5x?

a)

a = 3, b = -5, c = 4

b)

a = 3, b = 5, c = 4

c)

a = 3, b = 5, c = -4

d)

a = 3, b = -5, c = -4

6.

What's the axis of symmetry of y = 3x²- 6x + 4

a)

x=1

b)

x=-6

c)

x=2

d)

x=-1

7.

Find the vertex of
f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

8.

What is the vertex?

f\left(x\right)=\left(x-4\right)^2+3

a)

(-4,3)

b)

(4,3)

c)

(-4,-3)

d)

(4,-3)

9.

Which equation would shift the quadratic function

f\left(x\right)=x^2

up 3 units and to the right 4 units.

a)

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

b)

$f\left(x\right)=3\left(x-4\right)^2$

c)

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

d)

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

10.

Describe the transformation:

f\left(x\right)=\left(x+3\right)^2-2

a)

right 3, down 2

b)

up 3, left 2

c)

left 3, up 2

d)

left 3, down 2

11.

Write an equation of a quadratic that is translated down 2 units.

a)

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

b)

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

c)

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

d)

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

12.

Which quadratic would be the narrowest?

a)

$f\left(x\right)=\frac{1}{2}x^2$

b)

$f\left(x\right)=x^2$

c)

$f\left(x\right)=3x^2$

d)

$f\left(x\right)=5x^2$

13.

Given $f\left(x\right)=\frac{1}{4}x²$ how did we transform from the parent function?

a)

Vertical compression (wider)

b)

Vertical stretch (narrower)

c)

Vertical compression (wider) and reflection over x-axis

d)

Vertical stretch (narrower) and reflection over x-axis

14.

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

15.

In the vertex form f(x) = a(x - h)² + k , what does the 'a' value do?

a)

Shifts the function left or right

b)

Changing 'a' value has no affect on the parent function

c)

Vertical stretch or compression

d)

Shifts the function up or down

16.

Given f(x) = ax² , if 0 < a < 1 , the graph will transform by

a)

becoming wider or vertically compressed

b)

becoming narrower or vertically stretched

17.

In the vertex form f(x) = a(x - h)² + k , what does the 'h' value do?

a)

Shifts the function left or right

b)

Reflection over the x-axis

c)

Vertical stretch or compression

d)

Shifts the function up or down

18.

In the vertex form f(x) = a(x - h)² + k , what does the 'k' value do?

a)

Shifts the function left or right

b)

Reflects over the x-axis

c)

Vertical stretch or compression

d)

Shifts the function up or down

19.

How did we transform from y=x^2?

y = -3x²

a)

vertical reflection and vertical shift down

b)

vertical reflection and vertical stretch

c)

horizontal stretch

d)

vertical reflection and vertical compression

20.

Given f(x) = -x² , how did we transform from the parent function?

a)

Horizontal shift left

b)

Reflection over the x-axis

c)

Vertical shift down

d)

Vertical compression

21.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

22.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

23.

Factor: x² – 5x – 24

a)

(x - 5)(x + 19)

b)

(x - 8)(x + 3)

c)

(x - 3)(x + 8)

d)

(x - 19)(x + 5)

24.

Factor x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 25 ) ( x - 25 )

d)

Prime

25.

Factor x² + 5x + 4

a)

(x + 1)(x + 4)

b)

(x + 5)(x + 1)

c)

(x + 2)(x + 3)

d)

(x + 5)(x - 1)

26.

1 The discriminant is

a)

aX² + bX + c

b)

b - 4ac

c)

b² - 4ac

d)

b² + 4ac

27.

1 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

28.

2 For the function below, is the discriminant positive, negative, or zero?

y = x² + 4x + 4

a)

Positive

b)

Negative

c)

Zero

29.

2 A function has a discriminant of 4.

How many x-intercepts does it have?

a)

0

b)

1

c)

2

d)

4

30.

What is the discriminant and how many solutions would this quadratic have?

4x² + 6x - 4 = 0

a)

-28, No Solutions

b)

28, 2 Solutions

c)

100, 2 Solutions

d)

-100, No Solutions

31.

What is the discriminant and how many solutions would this quadratic have?

3x² + 3x + 4 = -3

a)

-75, No Solutions

b)

-75, 2 Solutions

c)

-39, No Solutions

d)

-39, 1 Solution

32.

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

a)

Maximum

b)

Minimum

33.

Which answer choice describes y = -3x² +7x - 2 accurately?

a)

opens up with a maximum

b)

opens up with a minimum

c)

opens down with a maximum

d)

opens down with a minimum

34.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

35.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

36.

12. Solve using any method.

(x - 2 )² -49 = 0

a)

5, 9

b)

^{-9, -5}

c)

9, -5

d)

^{9, -9}

37.

Solve the following quadratic equation...

x² + 3x + 2 = 0

a)

x = -1

x = -2

b)

x = 1

x = 2

c)

x = -1

x = 2

d)

x = 1

x = -2

38.

Using the graph solve the equation
-x²-2x+3=-5.

a)

{-3,-1}

b)

{-2,0}

c)

{-4,2}

d)

{-1,4}

39.

What is another word that describes the zeroes of a quadratic function?

a)

y-intercepts

b)

vertex

c)

x-intercepts

d)

maximum

40.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

41.

Solve using the Quadratic Formula:

x²+ 6x + 9 = 0

a)

x = −3, 3

b)

x = −3

c)

x = 3

d)

No Solution

42.

Complete the square.
x² + 6x + ____

a)

x² + 6x + 9

b)

x² + 6x - 36

c)

x² + 6x + 36

d)

x² + 6x - 9

43.

Complete the square for
x² + 12x + ____

a)

x² + 12x + 144

b)

x² + 12x + 36

c)

x² + 12x - 36

d)

x² + +12x - 144

44.

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

45.

Given the equation $x^2+18x=0$ how do you find the number to add to both sides to help you complete the square?

a)

Divide 18 by 2, then square that number and add it to both sides of the equation

b)

Square 18 and then add it both sides of the equation

c)

It already is a perfect square

d)

Subtract 18x from both sides and then divide both sides by x to find the answer

46.

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

a)

8 seconds

b)

1 second

c)

1.5 seconds

d)

1/4 second

47.

Heather dropped a water balloon over the side of her school building from a height of 80 feet. The approximate height of the balloon at any point during its fall can be represented by the following quadratic equation:

h = -16t² + 80

About how long did it take for the balloon to hit the ground?

a)

1.73 seconds

b)

2.24 seconds

c)

2.45 seconds

d)

2.83 seconds

Ch. 9 Quadratic Equations

Total questions: 47

Worksheet time: 2hrs 15mins

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