Free Printable standard, vertex, and factored form

1.

Which of the following shows
f(x) = x² + 12x - 2
written in vertex form?

a)

f(x) = (x + 6)² + 142

b)

f(x) = (x + 6)² - 34

c)

f(x) = (x + 6)² - 38

d)

hint: graph original function and find matching graph.

2.

Which of the following shows
f(x) = x² - 8x + 1
written in vertex form?

a)

f(x) = (x - 4)² - 15

b)

f(x) = (x - 4)² + 17

c)

f(x) = (x - 4)² - 17

d)

hint: graph original function and find matching graph

3.

If 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)

Hint: Graph and find vertex point.

4.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

5.

Determine the vertex of the parabola y=5(x-2)²–7

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

Hint: Graph and find the vertex point.

6.

$y=-3(x+5)^2-4$
Convert the equation from vertex form to standard form.

a)

y = 9x²- 15x + 21

b)

y = -3x²- 75x - 4

c)

hint: graph original function and find matching graph.

d)

y = -3x²- 30x - 79

7.

$y=-5(x+2)^2-10$
Convert the equation from vertex form to standard form.

a)

y = -5x²- 20x - 30

b)

y = -5x²- 4x - 10

c)

y = 25x² + 100x + 90

d)

hint: graph original function and find matching graph.

8.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

9.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

Hint: Graph and find line of symmetry

10.

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

11.

$Find\ the\ factored\ form\ of\ x^2+6x+\ 8$

a)

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

b)

(x +2) ( x- 4)

c)

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

d)

hint: graph original function and find matching graph.

12.

What is the factored form of

x² - 16x + 24

a)

(x + 2)(x - 14)

b)

(x - 2)(x - 12)

c)

(x + 16)(x - 2)

d)

hint: graph original function and find matching graph.

13.

What is the standard form of

(3x + 4)(3x – 4)

a)

9x²– 16

b)

9x² + 12x – 16

c)

9x²+ 24x – 16

d)

hint: graph original function and find matching graph.

14.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

15.

What is the equation for this parabola in factored form?

a)

y=(x+2)(x-1)

b)

y=(x-2)(x+1)

c)

y=(x-2)(x-1)

d)

y=(x+2)(x+1)

16.

What is the y-intercept?

f(x) = 3x²- 8 +5x

a)

(0, -8)

b)

(0, 5)

c)

(0, 3)

d)

hint: graph and find y intercept.

17.

What is the y-intercept of the following equation? f(x) = x²- 3x - 4

a)

(0,1)

b)

(0,-4)

c)

(0,3)

d)

hint: graph and find y intercept.

18.

What are the x-intercepts of the following quadratic function?

$y=\left(3x-6\right)\left(x+2\right)$

a)

x=-6 and x=-2

b)

x=6 and x= 2

c)

hint: graph and find x value of x intercepts

d)

x=-2 and x=2

19.

find solutions

a)

-4, 2

b)

-2, 4

c)

-16

d)

hint: graph and find x value of x intercepts

20.

find roots

a)

-3, 4

b)

3, 4

c)

-4, -3

d)

hint: graph and find x value of x intercepts

21.

What are the x-intercepts?

a)

0 and 2

b)

-4 and 0

c)

2 and 3

d)

0 and 4

22.

a)

-6, -2

b)

-2, 6

c)

2, 6

d)

-6, 2

23.

What is the equation for this parabola in factored form?

a)

y=(x+2)(x-1)

b)

y=(x-2)(x+1)

c)

y=(x-2)(x-1)

d)

y=(x+2)(x+1)

24.

Find the factors of 4x²-16x-9

a)

(2x-9)(2x+1)

b)

(2x+9)(2x-1)

c)

(4x-1)(x+9)

d)

hint: graph and find matching graphs

25.

What is the factored form of 25x²-9

a)

(5x+3)(5x-3)

b)

(x+5)(x-3)

c)

(x-3)(x+5)

d)

hint: graph and find matching graphs

26.

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

a)

Left 3 and up 5

b)

Right 3 and down 5

c)

Left 3 and down 5

d)

Right 3 and up 5

27.

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

a)

-f(x)

b)

f(-x)

c)

f^-1(x)

d)

f(2x)

28.

Identify the transformations.

a)

horizontal shift to the left 2 and vertical stretch by a factor of 3

b)

horizontal shift to the right 2 and vertical stretch by a factor of 3

c)

horizontal shift to the right 2 and vertical shrink by a factor of 3

d)

horizontal shift to the left 2 and vertical shrink by a factor of 3

29.

Match the equation to its description.

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

30.

g(x)=-f(x)
Describe the transformation to f(x) that results in g(x).

a)

f(x) has been reflected over the x-axis.

b)

f(x) has been reflected over the y-axis.

31.

Identify the coordinates of the point (3 , -2), translated 5 units left and 6 units up.

a)

(2,-4)

b)

(-2,4)

c)

(8,4)

d)

(-2,-8)

32.

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

a)

a translation shifting f(x) 4 units up

b)

a translation shifting f(x) 4 units down

c)

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

d)

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

33.

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

a)

Vertical Compression by a factor of 2

b)

Vertical Stretch by a factor of 2

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

34.

A student graphed f(x) = x and g(x) = f(x) - 12. Which statement is true?

a)

The graph of f is shifted 12 units to the right to create the graph of g.

b)

The graph of f is shifted 12 units down to create the graph of g.

c)

The graph of f is shifted 12 units up to create the graph of g.

d)

The graph of f is shifted 12 units to the left to create the graph of g.

35.

A student graphed f(x) = x and g(x) = f(x - 15). Which statement is true?

a)

The graph of f is shifted 15 units to the right to create the graph of g.

b)

The graph of f is shifted 15 units down to create the graph of g.

c)

The graph of f is shifted 15 units up to create the graph of g.

d)

The graph of f is shifted 15 units to the left to create the graph of g.

36.

Which of the following transformations are present (select all that apply)?

-2f(x - 1)) + 2

a)

reflection over horizontal axis

b)

Move up 2

c)

vertical stretch

d)

move right 1

e)

move left 1

37.

What is the equation of the function in the graph?

a)

$f(x)=∣x-3∣-2$

b)

$f(x)=-∣x+3∣+2$

c)

$f(x)=-∣x-3∣-2$

d)

$f(x)=∣x+3∣+2$

38.

Choose the equation that best matches the graphed function.

a)

$f(x)=|x|+2$

b)

$f(x)=|x|-2$

c)

$f(x)=-|x|$

d)

$f(x)=-|x|+2$

39.

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

a)

g(x) = (x + 3)²

b)

g(x) = (x - 3)²

c)

g(x) = x²+ 3

d)

g(x) = x²- 2

40.

.
The blue graphs is the parent function f(x)=|x|, the red must be

a)

g(x)=|x+2|

b)

g(x)=|x|+2

c)

g(x)=|x-2|

d)

g(x)=|x|-2

41.

Name the parent function.

a)

constant

b)

square root

c)

linear

d)

absolute value

42.

Name the parent function.

a)

quadratic

b)

cubic

c)

square root

d)

logarithmic

43.

Order the following functions from thinnest to widest based on the given factor.
1) f(x) = 5x²
2) f(x) = 1/2x²
3) f(x) = 3x²
3) f(x) = 1/3 x²

5) f(x) = -8x²

a)

5, 1, 3, 2, 4

b)

2, 4, 3, 1, 5

c)

1, 2, 5, 4, 3

d)

5, 2, 3, 4, 1

44.

Describe the transformations of the absolute value equation.

a)

Reflects over x-axis, compresses wider, shifts right 1 unit

b)

Reflects over x-axis, compresses wider, shifts up 1 unit

c)

Reflects over x-axis, stretches more narrow, shifts right 1 unit

d)

Reflects over x-axis, stretches more narrow, shifts up 1 unit

45.

What is the vertex of of the graph of this equation?
$y=8\left|x-3\right|+7$

a)

(3, 7)

b)

(8, 7)

c)

(-3, 7)

d)

(-3, 8)

46.

What is the vertex of the graph of this equation?
$y=-\left|x+6\right|$

a)

(-1, 6)

b)

(-6, 1)

c)

(-6, 0)

d)

(6, 0)

47.

Match the equation with the graph:

a)

y = (x - 1)² - 2

b)

y = (x + 1)² - 2

c)

y = (x - 2)² + 1

d)

y = (x + 2)² - 1

48.

Write an absolute value function given the following transformations:
Vertical Stretch of 2
Horizontal shift left 1 unit
Vertical shift down 9 units

a)

f(x) = |2x + 1| - 9

b)

f(x) = |2x - 1| - 9

c)

f(x) = 2|x + 1| - 9

d)

f(x) = 2|x - 1| - 9

49.

Which transformations are involved in the equation $y=\frac{1}{2}\sqrt{x+1}-1$ ?

a)

Horizontal translation left

b)

Vertical compression

c)

Vertical translation down

d)

Horizontal translation right

e)

Vertical stretch

50.

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

51.

What is the range of the graph?
Remember: Range is y!

a)

1 ≤ x ≤ 5

b)

1 < x < 5

c)

1 ≤ y ≤ 5

d)

1 < y < 5

52.

What is the DOMAIN of this graph?

a)

-4 ≤ x ≤ 3

b)

-1 ≤ x ≤ 4

c)

4 < x < 3

d)

-1 < x < 4

53.

What is the range of the function?

a)

-7≤x≤6

b)

-7<x<6

c)

-8<y<2

d)

-8≤y≤2

54.

What is the RANGE of this graph?

a)

y < -3

b)

y ≤ -3

c)

y > 1

d)

y ≥ 1

55.

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

a)

D: {1, -3, -4,}
R: {0, 1, 2, -4}

b)

D: {-4, 0, 1, 2}
R:{-4, -3, 1}

c)

D: {0, 1, 2, 3, 4}
R:{1, -3, -4}

d)

D: {0, 1, 2, -4}
R: {1, -3, -4, 1}

56.

What is the range?

a)

{-3, -1, 2, 4}

b)

{0, 4, 7}

c)

{0, 4, 4, 7}

d)

{7, 4, 0}

57.

Which graph does NOT pass the vertical line test?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

58.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

59.

A set of ordered pairs is called what?

a)

the domain

b)

a relation

c)

a function

d)

the range

60.

What is the domain of a relation?

a)

the set of all x-values

b)

the set of all y-values

61.

Which is the set of all y-values or the outputs?

a)

Domain

b)

Range

c)

Relation

d)

Function

62.

What is the range of the mapping?

a)

{1, 2, 4}

b)

{0, 1, 2, 3}

c)

{0, 3}

d)

{1, 4}

63.

Does the graph represent a function?

a)

Yes

b)

No

64.

Which relation has a domain of {3,7} and a range of {0,5} ?

a)

(3,5), (3,7), (0,5), (0,3)

b)

(3,0), (7,0), (3,5), (7,5)

c)

(3,0), (3,5), (3,7), (7,5)

d)

(7,0), (5,7), (3,5) (7,5)

65.

What transformations have occurred from $y\ =\ x^2$ ?

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

66.

Describe the transformation from

y\ =\ x^2

.

a)

left 2 up 5

b)

right 2 up 5

c)

left 2 down 5

d)

right 2 down 5

67.

Match the correct transformation from.
$y\ =\ x^2$
Moves up 2
Moves left 4

a)

A

b)

B

c)

C

d)

D

68.

In the equation f(x)=5(x+3)²-10 what does the 5 do?

a)

Vertical stretch by 5

b)

Horizontal compress by 5

c)

Reflect

d)

Move up 5

69.

Match the quadratic equation to its description of the transformation from the parent function, $y\ =x^2$ .

a)

Reflected over x, right 2 and up 1

b)

Reflected over x, left 2 and up 1

c)

Reflected over x, right 2 and down 1

d)

Reflected over x, left 2 and down 1

70.

How did we transform from the parent function?

g(x) = -1/5(x - 1)² + 7

a)

reflection across the y-axis, vertical compression by 1/5, right 1, up 7

b)

reflection across the x-axis, vertical compression by 1/5, right 1, up 7

c)

reflection across the y-axis, vertical stretch by 1/5, right 1, up 7

d)

reflection across the y-axis, vertical compression by 1/5, left 1, down 7

standard, vertex, and factored form

Total soal: 70

Worksheet time: 4hrs 32mins

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