Quiz about Analyzing Quadratic Functions

Question 1

Which function is in standard form?

Accepted Answer

g(x) = 4x² + 2x + 4

Answer

f(x) = -3x + 4

Answer

s(x) = 4(x + 1)² + 4

Answer

h(x) = -(x + 2)(x - 3)

Question 2

Which function is in factored form?

Accepted Answer

h(x) = -(x + 2)(x - 3)

Answer

g(x) = 4x² + 2x + 4

Answer

f(x) = -3x + 4

Answer

s(x) = 4(x + 1)² + 4

Question 3

What is the vertex of the parabola with the equation
f(x) = -2(x + 4)² - 3

Accepted Answer

(-4, -3)

Answer

(4, 3)

Answer

(-4, 3)

Answer

(4, -3)

Question 4

What is the vertex of the parabola with the equation
f(x) = -2(x - 4)² - 3

Accepted Answer

(4, -3)

Answer

(-4, -3)

Answer

(4, 3)

Answer

(-4, 3)

Question 5

What are the x-intercepts of the parabola with the equation
g(x) = 2(x - 3)(x - 4)

Accepted Answer

(3,0) , (4,0)

Answer

(0,3) , (0,4)

Answer

(-3,0) , (-4,0)

Answer

(0,-3) , (0,-4)

Question 6

Which function has a minimum?

Accepted Answer

f(x) = 2x² + 3x + 4

Answer

f(x) = -2x² + 3x + 4

Answer

f(x) = -(x - 4)(x - 5)

Answer

f(x) = -4(x - 2)² + 4

Question 7

The axis of symmetry go through the vertex.

Accepted Answer

True

Answer

False

Question 8

f(x) = -2x² + 3x + 1
What is f(1)?

Accepted Answer

2

Answer

1

Answer

0

Answer

-3

Question 9

What is another word for zeros?

Accepted Answer

roots

Answer

y-intercepts

Answer

vertex

Answer

axis of symmetry

Question 10

Does this graph have a maximum or minimum value?

Accepted Answer

minimum

Answer

maximum

Answer

neither

Answer

both

Question 11

Use the graph to determine the solutions.

Accepted Answer

1 and 3

Answer

-1 and -3

Answer

1 and -3

Answer

-1 and 3

Question 12

What are the x-intercepts?

Accepted Answer

0 and 4

Answer

0 and 2

Answer

-4 and 0

Answer

2 and 3

Question 13

What is the vertex of the quadratic function: y=1/2(x-3)²+8?

Accepted Answer

(3,8)

Answer

(-3,-8)

Answer

(-3,8)

Answer

(3,-8)

Question 14

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

Accepted Answer

No Real Solution

Answer

1 Real Solution

Answer

2 Real Solutions

Answer

Half a Solution

Question 15

Determine if the function graphed has a maximum or a minimum value and identify that value.

Accepted Answer

maximum at 4

Answer

maximum at -1

Answer

minimum at -1

Answer

minimum at 4

Question 16

How many solutions does this graph have?

Accepted Answer

no solutions

Answer

one

Answer

two

Answer

cannot be determined

Question 17

What is the axis of symmetry?

Accepted Answer

the dividing line for a parabola

Answer

the slope of the graph

Answer

a way to spin my pencil

Answer

the x-axis

Question 18

The point in which a graph hits the x-axis is know as the _____

Accepted Answer

All answers are correct

Answer

Solution

Answer

x-intercept

Answer

Root

Question 19

What are the roots of the function
f(x)= (x - 2)(x + 3)?

Accepted Answer

x = 2 or x = -3

Answer

x = - 2 or x = 3

Answer

The are no real roots

Answer

x = 2 or x = 3

Question 20

What is the axis of symmetry of the given function?

Accepted Answer

x = 1

Answer

y = 1

Answer

y = -1

Answer

x = -1

Question 21

Identify the vertex and whether the graph opens up or down.

Accepted Answer

(1, 4); opens down

Answer

(-1, 4); opens up

Answer

(-1, 4); opens down

Answer

(1, 4); opens up

Question 22

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

Accepted Answer

x = -3

Answer

y = -2

Answer

x = 3

Answer

y = 2

Question 23

Write the equation of the quadratic in vertex form given the following:

vertex: (4, -2)

point: (0,-6)

opens down

Accepted Answer

f(x)=-1/4(x-4)²-2

Answer

f(x)=(x-4)²-2

Answer

f(x)=-4(x-4)²-2

Answer

f(x)=1/4(x+4)²-2

Question 24

Write the equation of the quadratic in vertex form given the following:

axis of symmetry: x=1

Points: (2, 5) (-2, 21)

Accepted Answer

f(x)=2(x-1)²+3

Answer

f(x)=(x-1)²+5

Answer

f(x)=1/2(x-1)²+3

Answer

f(x)=2(x-1)²-3

Question 25

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

Accepted Answer

vertical shift up 5 units

Answer

horizontal shift right 5 units

Answer

horizontal shift left 5 units

Answer

vertical shift down 5 units

Question 26

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

Accepted Answer

horizontal shift left 7 units

Answer

horizontal shift right 7 units

Answer

vertical shift up 7 units

Answer

vertical shift down 7 units

Question 27

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

Accepted Answer

Vertical stretch by a factor of 5

Answer

Vertical compress by a factor of 5

Answer

Reflect over x-axis

Answer

Vertical shift up 5 units

Question 28

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

Accepted Answer

a horizontal shift 4 units to the left

Answer

a vertical shift 4 units up

Answer

a vertical shift 4 units down

Answer

a horizontal shift 4 units to the right

Question 29

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

Accepted Answer

Vertical Stretch by a factor of 2 and vertical shift up 4 units

Answer

Vertical Compress by a factor 2 and vertical shift up 4

Answer

Vertical Stretch by a factor of 2 and horizontal shift left 4 units

Answer

Vertical Compress by a factor of 2 and horizontal shift right 4 units

Question 30

What is the equation of the quadratic function obtained from vertically stretching the parent function by a factor of 2 and then vertically shifting up 3 units?

Accepted Answer

f(x)= 2x²+3

Answer

f(x)= 2(x-3)²

Answer

f(x)= 2(x+3)²

Answer

f(x)= (x-2)²+3

Question 31

What is the equation of the quadratic function obtained from horizontally shifting the parent function 17 units left and then reflecting across the x-axis?

Accepted Answer

f(x)= -(x+17)²

Answer

f(x)= -x²-17

Answer

f(x)= -(x-17)²

Answer

f(x)= -x²+17

Question 32

If the blue graph is
f(x) = x²the red must be...

Accepted Answer

g(x) = (x - 3)²

Answer

g(x) = (x + 3)²

Answer

g(x) = x²+ 3

Answer

g(x) = x²- 2

Question 33

The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?

Accepted Answer

(-6, 5)

Answer

(-2, 5)

Answer

(-4, 3)

Answer

(-4, 7)

Question 34

Identify the transformation from the graph of f(x)=x²to the graph g(x)= -(x+5)²

Accepted Answer

shifted left 5 units

reflection x-axis

Answer

shifted left 5 units

reflection y-axis

Answer

shifted down five units

reflection in x-axis

Answer

shifted right 5 units

reflection x-axis

Question 35

What equation represents the quadratic function?

Accepted Answer

y = (x - 1)² - 4

Answer

y = (x - 4)² + 1

Answer

y = (x + 1)² - 4

Answer

y = (x - 4)² - 1

Question 36

What equation represents the quadratic function?

Accepted Answer

y = -(x + 3)² + 10

Answer

y = -(x - 3)² + 10

Answer

y = (x + 3)² + 10

Answer

y = (x + 10)² - 3

Question 37

Match the equation to its description.

Accepted Answer

Reflected over x and stretched by 3

Answer

Stretched by 3

Answer

Reflected over x

Answer

Reflected over x and up 3

Question 38

Match the equation to its description.

Accepted Answer

Reflected over x, right 2 and up 1

Answer

Reflected over x, left 2 and up 1

Answer

Reflected over x, right 2 and down 1

Answer

Reflected over x, left 2 and down 1

Question 39

If red represents y = x², which equation represents black?

Accepted Answer

y = -7x2

Answer

y = 7x2

Answer

y = -(1/7)x²

Answer

y = -5x2

Question 40

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

Accepted Answer

It is the vertex

Answer

It is an x-intercept

Answer

It is the y-intercept

Answer

It is the axis of symmetry

Question 41

What is the significance of the ordered pair (0, -2) to the graph?

Accepted Answer

It is the y-intercept

Answer

It is the vertex

Answer

It is an x-intercept

Answer

It is the axis of symmetry

Analyzing Quadratic Functions

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