Free Printable Quadratic Trans/Standard Form

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Quadratic Trans/Standard Form

Total questions: 40

Worksheet time: 1hrs 12mins

Name

Class

Date

Match the equation to its description.

Reflected over x and up 4

Reflected over x and down 4

Reflected over x and right 4

Reflected over x and left 4

Match the equation to its description.

Stretched by 2 and up 4

Compressed by 2 and up 4

Stretched by 2 and left 4

Compressed by 2 and left 4

What is the vertex form of a quadratic function?

f(x) = 2a(x-h)² + k

f(x) = a(x-h)² + k

f(x) = (x+h)² + k

f(x) = a(x-h) - k

Identify the vertex of f(x) = -2(x+1)² + 3

(h,k)

(3, 1)

(-1,-3)

(-1,3)

Does the function y = (x+2)² have a maximum or minimum?

Maximum

Minimum

Both

Neither

Does the function y = -1/2(x+1)² have a maximum or minimum?

Maximum

Minimum

Both

Neither

What does the quadratic function that has a vertex of (3,4) look like?

y = a(x+3)² + 4

y = a(x-3)² + 4

y = -a(x+3) - 4

y = a(x-3)² - 4

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

Compress by 2, shifted 2 units left and 5 down

Stretch by 5, shifted 5 units left and 2 down

Stretch by 2, shifted 2 units left and 5 down

Compress by 5, shifted 2 units left and 2 down

What steps transform the graph y = x² to y = -1/2(x-4)² + 1?

Compressed by 1/2, shifted 4 units right and 1 unit up

Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

Stretched by 1/2, shifted 4 units right and 1 unit down

10.

Which of the following equations matches standard form of a quadratic?

ax + by = c

y = a(x - h)² + k

y = ax² + bx + c

y = mx + b

11.

The graph of a quadratic function is called a

Parabola

Vertex

Axis of Symmetry

Vertex Form

12.

What is the vertex?

(2, 4)

(3, -1)

(0, 8)

(4, 2)

13.

Does the equation open or or down?
Y = -3x² +7x - 2

down

14.

Determine the range of the function: f(x) = 2x² - 9

[-9, ∞)

[1.15, ∞)

(∞, 1.15]

(∞, -9]

15.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

(5, -7)

(-2, -7)

(2, -7)

(-7, -2)

16.

Write the equation of the quadratic in vertex form given the following:
vertex: (4, -2)
point: (0,-6)
opens down

f(x)=(x-4)²-2

f(x)=-4(x-4)²-2

f(x)=1/4(x+4)²-2

f(x)=-1/4(x-4)²-2

17.

What is the green dot on the parabola called?

maximum

minumum

roots

zeros

18.

Does this parabola have a maximum or minimum?

Maximum

Minimum

19.

Identify a, b, and c if y = +3x²+5x - 8

a=3, b=5, c= - 8

A=3, B=-8, C=5

A=3x², B=5x, C=-8

A=3x² , B=-8, C=5x

20.

What is the "b" term of this equation? y = 2x² - 5x + 10

-5

21.

Which of the following equations does not represent a quadratic function?

$y\ =\ -2x^2\ +\ 10x\ -9$

$y\ =\ x^2$

$y\ =\ 3\left(x\ +\ 4\right)^2\ -5$

$y\ =\ 5x\ +\ 12$

22.

How many zeros does this parabola have?

23.

Which equation matches the graph?

$y=2x^2+8x-5$

$y=2x^2-8x-5$

$y=-2x^2+8x-5$

$y=2x^2+8x+5$

24.

Which graph matches the equation below?

y=3x^2-6x-2

25.

Find the a, h, and k values for the graph.

a = -2; h = -3; k = 4

a = -2; h = 3; k = 4

a = -2; h = 4; k = -3

a = -2; h = 4; k = 3

26.

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

Horizontal shift left 6, vertical shift up 2

Horizontal shift left 6, vertical shift down 2

Horizontal shift right 6, vertical shift down 2

Horizontal shift right 6, vertical shift up 2

27.

If the blue is f(x)=x^2,the red must be

g(x)=(x+3)²

g(x)=(x-3)²

g(x)=x²+3

g(x)=x²-2

28.

If the blue is f(x)=x^2,then the red must be

g(x)=x²- 5

g(x)=x²+ 5

g(x)=(x - 5)²

g(x)=(x + 5)²

29.

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

a translation shifting f(x) 4 units up

a translation shifting f(x) 4 units down

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

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

30.

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

(-2, 16)

(2, 0)

(2, 4)

(-2, 4)

31.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a = 4, b = -8, c = 3

a = 4, b =-8, c =-3

a = 4, b = 8, c = 3

a = 4, b = 8, c = -3

32.

What are the x- intercepts?

x= 0 and x= -4

x= 0 and x= 4

y= 0

x= 2

33.

What is the vertex?
f(x) = -x²- 4x + 12.

(-2, 16)

(2, 0)

(2, 4)

(-2, 4)

34.

The axis of symmetry line passes through which point?

y-intercept

any random point

vertex

symmetrical point for the vertex

35.

What is the equation for axis of symmetry?

y=3

x=3

x=5

x=1

36.

What is the axis of symmetry?
f(x) = x²- 8x + 15.

x = -4

x = 4

y = 4

y = -4

37.

Identify a, b, and c if y=3x²-8+5x. Be careful! :-)

A=3, B=5, C=-8

A=3, B=-8, C=5

A=3x², B=5x, C=-8

A=3x² , B=-8, C=5x

38.

What is another word for the zeros of a function?

y-intercepts

x-intercepts

vertex

axis of symmetry

39.

What are the x-intercepts of the parabola?
y = ¼(x + 2)(x - 6)

-2 and 6

2 and -6

-2

¼ and -2 and 6

40.

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

f(x) = (x + 6)² + 142

f(x) = (x + 6)² - 34

f(x) = (x + 6)² - 38

f(x) = (x + 6)² + 34

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Quadratic Trans/Standard Form

Total questions: 40

Worksheet time: 1hrs 12mins

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