M4 L21: Transforming Quadratics

M4 L21: Transforming Quadratics

By Lora Lyons

Draw

Example 1: Write the completed-square (VERTEX FORM) of the quadratic function:

$$g\left(x\right)=2x^2+12x+1$$  

Multiple Choice

Example 1a:

Where is the vertex of the graph of this function located?

(refer to your equation from example 1)

• (3, -17)

• (-3, -17)

Draw

The quadratic parent function has been translated:

3 units to the right

vertically stretched by a factor of 4

moved 2 units up

Write the equation for the transformed graph.

Multiple Choice

Write a formula that describes the transformation from the quadratic parent function:

Shift three units to the right

• $$y=\left|x+3\right|$$  

• $$y=\left(x+3\right)^2$$  

• $$y=\left|x\right|+3$$  

• $$y=\left(x-3\right)^2$$  

Multiple Choice

Write a formula that describes the transformation from the quadratic parent function:

Vertical Shrink by a factor of 0.5 (1/2)

• $$y=x^2-\frac{1}{2}$$   

• $$y=\frac{1}{2}x^2$$   

Multiple Choice

Write a formula that describes the transformation from the quadratic parent function:

Reflection across the x axis

• $$y=-x^2$$    

• $$y=\left(x+1\right)^2$$    

Multiple Choice

Write a formula that describes the transformation from the quadratic parent function:

4 units up

• $$y=\left(x+4\right)^2$$     

• $$y=x^2+4$$