Free Printable Quadratic Basics Practice

1.

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

a)

Max

b)

Vertex

c)

Axis of Symmetry

d)

Intercept

2.

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

3.

Which is these equations is a quadratic function?

a)

f(x)=2x+5

b)

f(x)=2^x

c)

f(x)=(x+1)³

d)

f(x)=(x-5)²

4.

A point on a graph that has the coordinates (0,___) is called a...

a)

x-intercept

b)

vertex

c)

maximum

d)

y-intercept

5.

The curved graph of a quadratic (the U shape)

a)

Quadratic

b)

Parabola

c)

Vertex

d)

Minimum

6.

Find the equation of the parabola that has moved...

5 units to the right

a)

y=x^2+5

b)

$y=x^2-5$

c)

$y=\left(x+5\right)^2$

d)

$y=\left(x-5\right)^2$

7.

Find the equation of the parabola that has moved...

8 units down

a)

$y=x^2+8$

b)

$y=x^2-8$

c)

$y=\left(x+8\right)^2$

d)

$y=\left(x-8\right)^2$

8.

Find the equation of the parabola that has moved...

3 units up

a)

y=x^2+3

b)

$y=x^2-3$

c)

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

d)

$y=3x^2$

9.

Find the equation of the parabola that has moved...

5 units to the left

a)

$y=x^2+5$

b)

$y=x^2-5$

c)

$y=\left(x+5\right)^2$

d)

$y=\left(x-5\right)^2$

10.

Find the equation of the parabola that has...

stretched by factor of 3

a)

y=3x^2

b)

$y=\frac{1}{3}x^2$

c)

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

d)

$y=x^2+3$

11.

Find the equation of the parabola that has...

compressed by factor of 3

a)

y=3x^2

b)

$y=\frac{1}{3}x^2$

c)

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

d)

$y=x^2+3$

12.

Find the equation of the parabola that has been...

reflected

a)

y=-x^2

b)

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

c)

$-y=x^2$

d)

$y=x^2-1$

13.

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

a)

y=\left(x+3\right)^2+5

b)

$y=\left(x+5\right)^2+3$

c)

$y=\left(x-3\right)^2+5$

d)

$y=\left(x+5\right)^2-3$

14.

Find the equation of the parabola that has...

been reflected

stretched by 5

a)

$y=-5x^2$

b)

$y=-\frac{1}{5}x^2$

c)

$-y=5x^2$

d)

$-y=\frac{1}{5}x^2$

15.

Find the equation of the parabola that has...

moved 4 units down

been compressed by factor of 3

a)

y=\frac{1}{3}x^2-4

b)

$y=3x^2-4$

c)

$y=\frac{1}{3}\left(x+4\right)^2$

d)

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

16.

Find the equation of the parabola that has...

been stretched by 2

moved 5 units to the right

moved 3 units down

a)

$y=2\left(x-5\right)^2-3$

b)

$y=2\left(x+5\right)^2-3$

c)

$y=\frac{1}{2}\left(x+5\right)^2-3$

d)

$y=\frac{1}{2}\left(x-5\right)^2-3$

17.

Find the equation of the parabola that has...
been reflected
compressed by 4
moved 7 units up

a)

$y=-\frac{1}{4}x^2+7$

b)

$y=-4x^2+7$

c)

$y=-\frac{1}{4}\left(x+7\right)^2$

d)

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

18.

Find the equation of the parabola that has...

compressed by factor of 2

moved 3 units to the left

moved 4 units up

a)

y=\frac{1}{2}\left(x+3\right)^2+4

b)

$y=\frac{1}{2}\left(x-3\right)^2+4$

c)

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

d)

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

19.

Find the equation of the parabola that has...

been reflected

stretched by 4

moved 5 units to the right

moved 6 units down

a)

y=-4\left(x-5\right)^2-6

b)

$y=-4\left(x+5\right)^2-6$

c)

$y=-\frac{1}{4}\left(x+5\right)^2-6$

d)

$y=4\left(x-5\right)^2-6$

20.

Find the equation of the parabola that has...

been reflected

compressed by factor of 2

moved 3 units to the left

moved 4 units up

a)

y=-\frac{1}{2}\left(x+3\right)^2+4

b)

$y=-\frac{1}{2}\left(x-3\right)^2+4$

c)

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

d)

$y=\frac{1}{2}\left(x+3\right)^2+4$

21.

Name the x-intercept(s)?

a)

(0, 0)

b)

(2, 4)

c)

(0, 0) and (0, 4)

d)

(0, 0) and (4, 0)

22.

What is the vertex of the graph?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

23.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

24.

Is this point a max or min?

a)

max

b)

min

25.

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

a)

(4,0)

b)

(-4,0)

c)

(0,-4)

d)

(0,4)

26.

What is another name for the x-intercepts of a quadratic?

a)

y-intercept

b)

Zeros

c)

x-axis

d)

They don't have another name

27.

What is the vertex of y=x²+4x+3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

28.

What is the axis of symmetry of y=2x²-4x+9?

a)

x = 1

b)

x = -1

c)

x = -2

d)

x = 4

29.

How many solutions does this graph have?

a)

one

b)

two

c)

no solutions

d)

all real numbers

30.

Find the roots of y=5x²+7x-90

a)

(-5,0)(3.6,0)

b)

(0,-5)(0,3.6)

c)

(-4,0)(4,0)

d)

(-5,0)

31.

What is the axis of symmetry?

f(x)=-3(x+1)^2-5

a)

x = -5

b)

x = 1

c)

x = -1

d)

x = 3

32.

What is the axis of of symmetry for the equation

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

a)

x = 3

b)

x = -3

c)

x = 2

d)

x = 4

33.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

34.

Is this point a max or min?

a)

max

b)

min

35.

What is the vertex?

a)

(-3, 0)

b)

(3, 0)

c)

(0, 18)

d)

(18, 0)

36.

What is the significance of the ordered pair (2, -4) to the graph?

a)

It is the vertex

b)

It is an x-intercept

c)

It is the y-intercept

d)

It is the axis of symmetry

37.

Which statement about the graph is FALSE?

a)

The vertex is (-3, 18)

b)

The vertex is a maximum

c)

The y-intercept is y = 0

d)

The axis of symmetry is y = -3

38.

Another name for the x-intercept

a)

Roots

b)

Zeros

c)

Solutions

d)

All of the above

39.

Where the parabola crosses the y-axis.

a)

X-intercept

b)

Domain

c)

Y-intercept

d)

Axis of Symmetry

40.

On the graph, what does the coordinate (0, -2) represent?

a)

the x-intercept

b)

the minimum

c)

the axis of symmetry

d)

the y-intercept

41.

The maximum or minimum point of a parabola, the point the axis of symmetry cuts through, is called

a)

point of inflection

b)

origin

c)

vertex

d)

starting point

42.

What is the orange line called?

a)

Line of Solutions

b)

Roots

c)

Vertex

d)

Axis of Symmetry

43.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

44.

What is this?

a)

Quadratic Formula

b)

Quadratic Parent Function

c)

Quadratic Standard Form

d)

Quadratic Vertex Form

45.

What is this?

a)

Quadratic Formula

b)

Quadratic Parent Function

c)

Quadratic Standard Form

d)

Quadratic Vertex Form

46.

What is this?

a)

Quadratic Parent Function

b)

Quadratic Standard Form

c)

Quadratic Vertex Form

d)

Quadratic Formula

47.

Which letter determines if a parabola opens up or down?

a)

a

b)

b

c)

c

48.

What is the range of the function?

*Hint: Range is all of the y-values included in the function.

a)

-6 ≤ y ≤ 3

b)

y ≥ 3

c)

All real numbers

d)

y ≤ 3

49.

Given the equation y = 3(x + 5)² - 4,

what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

50.

Given the equation: y = -(x - 4)²- 3,

does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

51.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

52.

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

Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

53.

What piece of information does c identify in the following equation?

y = ax²+ bx + c

a)

Zeroes

b)

Axis of Symmetry

c)

Direction

d)

y-intercept

54.

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

55.

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.

56.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

57.

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

58.

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

h(t) = -16t² + 8t + 24

When would you reach 16 feet above the water?

a)

8 seconds

b)

1 second

c)

1/2 second

d)

1/4 second

59.

The profit from selling local ballet tickets depends on the ticket price. Using past receipts, we find that the profit can be modeled by the function:

p= -15x² +600x +60

What is the maximum profit you can make from selling tickets?

a)

$6060

b)

$20

c)

$600

d)

$10,250

60.

Identify a, b and c in the quadratic equation: $2x^2-3x-5=0$

a)

a = 2 , b = 3, c = -5

b)

a = 2, b = -3, c = 5

c)

a = 2, b = -3, c = -5

d)

a = -2, b = 3, c = 5

61.

$b^2-4b+4=0$

a)

x = -2

b)

x = 2

c)

no real solution

d)

x = -2 and 2

62.

$m^2-5m-14=0$

a)

x = 7 and -2

b)

x = 7 and 2

c)

x = -7 and -2

d)

x = -7 and 2

63.

$x^2+4x+3=0$

a)

x = 1 and -3

b)

x = -1 and -3

c)

x = -1 and 3

d)

x = 1 and 3

64.

$2x^2-2x+3=0$

a)

x = -1 and 3

b)

x = 1 and -3

c)

No real solution

d)

x = 1

65.

What are the roots to $4x^2-35x+29=0$ ?

a)

x = 0 & 0.927

b)

x= 0.972 & 29

c)

x = 0.927 & 7.823

d)

x = 29 & -35

66.

What are the solutions to $n^2+2n-24$ ?

a)

-8,3

b)

-4,6

c)

12,-2

d)

-6,4

67.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

68.

Factor
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

69.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

70.

Factor
v² - 6v + 9

a)

(v-3)²

b)

(v-6)²

c)

(v-9)(v+6)

d)

not factorable

71.

Factor
r² -16r + 60

a)

(r - 15)(r + 4)

b)

(r - 6)(r + 10)

c)

(r - 6)(r - 10)

d)

(r +30)(r - 2)

Quadratic Basics Practice

Total questions: 71

Worksheet time: 3hrs 47mins

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