Transformations of Absolute Value and Quadratic Functions

Open Ended

Today you had an English Exam, How was it? :D :D

Labelling

Label the Horizontal and Vertical Direction

Drag labels to their correct position on the image

Horizontal

Vertical

Hotspot

you are at y=-2 where would you be if you moved 6 steps in the positive vertical direction?

Labelling

put the correct label in the right place

Drag labels to their correct position on the image

Horizontal Negative

Horizontal Positive

Vertical positive

Vertical Negative

Hotspot

Start from 2 and do horezental transition of 3 units to the left

Match

Match the following

Reflection

Transition

Rotation

• Reflection

• Transition

• Rotation

Multiple Choice

Name the parent function family.

$$y=\left|x-2\right|+7$$  

• Smith

• Constant
  

• Identity
  

• Absolute Value
  

• Quadratic

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​https://www.geogebra.org/m/mjcqp7t8

Multiple Choice

What is the parent absolute value function represented in the image?

• f(x) = |x|

• f(x) = x^2

• f(x) = -x

• f(x) = x + 1

Multiple Choice

The graph of the absolute value parent function, $$f\left(x\right)=\left|x\right|$$ is shown below, including three key points that lie on the graph.

If $$g\left(x\right)=2\left|x-3\right|+1$$ , which of the following are the coordinates of the three transformed key points?

• $$\left(-12,\ 4\right);\ \left(-6,\ 1\right);\ \left(0,\ 4\right)$$

• $$\left(-9,\ 4\right);\ \left(-3,\ 1\right);\ \left(3,\ 4\right)$$

• $$\left(0,\ 7\right);\ \left(3,\ 1\right);\ \left(6,\ 7\right)$$

• $$\left(-6,\ 7\right);\ \left(-3,\ 1\right);\ \left(0,\ 7\right)$$

Multiple Choice

Identify the equation of the graph.

• $$f\left(x\right)=-\left(x+4\right)^2+2$$
  

• $$f\left(x\right)=\left(x-4\right)^2+2$$
  

• $$f\left(x\right)=\left|x+4\right|+2$$

• $$f\left(x\right)=\left|x-4\right|+2$$

• $$f\left(x\right)=-\left|x+4\right|+2$$

Categorize

Options (11)

Compression of 2

Stretch of 2

Shift left 2

Shift right 2

Shift down 5

Shift up 5

Shift left 4

Shift right 4

Stretch of 5

Compression of 5

Reflection

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

Steps

Not an answer

Multiple Choice

Describe the transformation in the image

• Translation

• Reflection

• Rotation

Open Ended

Use an AI tool to create your own problem and share it the the class :D

Multiple Choice

Name the parent function family.

$$f\left(x\right)=\left(x-1\right)^2+3$$  

• Jones

• Constant
  

• Identity
  

• Absolute Value
  

• Quadratic

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Multiple Choice

Identify the equation of the graph.

• $$f\left(x\right)=\left(x+4\right)^2+2$$
  

• $$f\left(x\right)=\left(x-4\right)^2+2$$
  

• $$f\left(x\right)=\left|x+4\right|+2$$

• $$f\left(x\right)=\left|x-4\right|+2$$

Multiple Select

Identify the transformation 

(select all that apply).

$$f\left(x\right)=\left|x+3\right|-2$$  

• Left 3

• Right 3

• Up 2

• Down 2

Multiple Choice

What is the purpose of the Absolute Value Transformations Simulator?

• To teach basic arithmetic

• To demonstrate absolute value transformations

• To simulate geometric shapes

• To solve algebraic equations

Multiple Select

Identify the transformation 

(select all that apply).

$$y=x^2-5$$  

• Left 5

• Right 5

• Up 5

• Down 5

Multiple Choice

  The blue function is the original function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Multiple Choice

  . 
The blue is f(x)=|x|, red must be

• g(x)=|x+2|
• g(x)=|x|+2
• g(x)=|x-2|
• g(x)=|x|-2

Multiple Choice

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

• g(x)=f(x)-5

• g(x)=f(x)+5

• g(x)=f(x-5)

• g(x)=f(x+5)

Open Ended

Describe how to transform the graph of the parent absolute value function f (x) = |x| to obtain the graph of the function g(x) = -2f(1/4(x + 1)) - 3.

Multiple Choice

Which transformations occur inside the function f and which occur outside of f?

• vertical stretch by a factor of 2 and reflection across the x-axis

• horizontal stretch by a factor of 4

• horizontal translation left 1 unit

• vertical translation down 3 units

Multiple Choice

The graph of the function p(x) is represented below. On the same set of axes, sketch the function p(x + 2).

Multiple Choice

What is the transformation?

• Vertical Translation up 2
• Vertical Translation down 2
• Horizontal Translation left 2
• Horizontal Translation right 2

Fill in the Blank

The equations $$f\left(x\right)=a\left(x-h\right)^2+k$$  represents the graph shown:

What are the values for h and k?

Type your answers for h,k separated by a comma.

Multiple Choice

What should you remember to do after class?

• Study the lesson

• Play games

• Watch TV

• Go out with friends

Multiple Choice

Identify the equation of the graph.

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

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

• $$f\left(x\right)=-\left|x+3\right|+5$$

• $$f\left(x\right)=\left|x+3\right|+5$$

Multiple Choice

What does the acronym STEM stand for?

• Science, Technology, Engineering, Math

• Science, Technology, English, Math

• Science, Technology, Engineering, Medicine

• Science, Technology, Engineering, Management

Quadratic Transformation - Vertical and Horizontal Shifts (separate) - Maze chase

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Multiple Choice

Describe the change shown in the graph and equation. f(x) is the parent function and g(x) is the new function

f(x)= x²

g(x)= (x−3)²

• Vertex moves 5 up

• Vertex moves 3 down

• Vertex moves 3 to the right

• Stretched by a factor of 3

Multiple Choice

Identify the equation of the graph.

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

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

• $$f\left(x\right)=\left|x+4\right|+3$$

• $$f\left(x\right)=\left|x-4\right|+3$$

Open Ended

Share one thing you learned during this lesson :)

Poll

How confident do you feel about this topic now?

• Very confident
• Somewhat confident
• Not confident

Schoology - Class Work

WEEK 7 - Period 5