Quadratic and Absolute Value Translations

• Equation has highest power of 2

• makes U-shaped graph (Parabola)

• has a vertex (turning point)

• zeros are the solutions

​

Quadratic

• Equation has x in absolute value lines |x|

• makes v-shaped graph

• has a vertex (turning point)

• zeros are the solutions

​​Absolute Value

Multiple Choice

Name the parent function.

• quadratic
• cubic
• square root
• logarithmic

Multiple Choice

The graph of a quadratic function is called a

• Parabola
• Vertex
• Axis of Symmetry 
• Vertex Form

Multiple Choice

What is the vertex of the absolute value function?

• (4, 0)
• (0, 4)
• (-infinity, infinity)
• [4, infinity)

Multiple Choice

What type of shape is an absolute value function?

• Line
• V
• U
• Z

Multiple Choice

Does this graph have a maximum or minimum?

• Minimum
• Maximum

Multiple Choice

What is the equation for axis of symmetry?

• y=3
• x=3
• x=5
• x=1

Multiple Choice

Which best describes the vertex?

• Any point on the parabola/absolute value graph.

• A point on the x-axis.
• The highest or lowest point of a parabola/absolute value graph.

• A point on the y-axis.

ADD after |x| shifts UP




SUBTRACT after |x| shifts down​

​Vertical Shifts

Multiple Choice

Describe the transformation of the equation below:

y = I x |+ 3

• Left 3

• Right 3

• Up 3

• Down 3

Multiple Choice

What is the equation of the absolute value function?

• f(x)= |x+4|
• f(x)= |x-4|
• f(x)= |x| + 4
• f(x)= |x| - 4

Multiple Choice

What is the transformation shown below:

$$y=\left|x\right|-5$$

• Shifts left 5

• Shifts right 5

• Shifts up 5

• Shifts down 5

Multiple Choice

. 
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

ADD in the grouping symbols () || move LEFT



SUBTRACT in the grouping symbols () || move RIGHT.

​

Horizontal Shifts

Multiple Choice

What is the equation of the graph below?

• f(x) = I x + 2 I 
• f(x) = I x + 2 I +2
• f(x) = I x - 2 I +2
• f(x) = I x - 2 I 

Multiple Choice

Describe the transformation of the equation below:

y = I x + 3 I

• Left 3

• Right 3

• Up 3

• Down 3

Multiple Choice

Describe the transformation of the equation below from the parent function of
$$y=\left|x-4\right|$$

• Left 4
• Right 4
• Up 4
• Down 4

Drag and Drop

y = |

Placeholder

| +​

Placeholder

Drag these tiles and drop them in the correct blank above

moves left or right

moves diagonally

Multiple Choice

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Multiple Choice

Which of the following equations represents $$f\left(x\right)=x^2$$  after being transformed by 3 to the right and down 10

• f(x)= x + 13

• f(x) = (x + 10)² + 3

• f(x) = (x - 3)² - 10

• f(x) = x - 13

Multiple Choice

Match the equation to its description

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

• Right 2 and up 2

• Right 2 and down 2

• Left 2 and up 2

• Left 2 and down 2

Multiple Choice

What equation represents the quadratic function?

• y = (x - 5)² - 3
• y = (x - 5)² + 3
• y = (x + 5)² - 3
• y = (x - 3)² - 5

Multiple Choice

What equation represents the quadratic function?

• y = (x - 7)² - 2
• y = (x + 7)² + 2
• y = (x + 7)² - 2
• y = (x + 2)² + 7

Multiple Choice

What shifts have occurred?

• left 1, up 5
• left 1, down 5
• right 1, down 5
• right 1, up 5

Multiple Choice

Which of the following describes the horizontal and vertical translations of the following functions:
f(x) = |x + 4| - 9

• Left 4
  up 9
• Left 4
  Down 9
• Right 4
  up 9
• Right 4
  Down 9

Open Ended

Describe the movement of quadratic and absolute value graphs in your own words.