Quadratic Transformations

Quadratic Transformations

Warm-up

 $y=\pm a\ \left(x\pm h\right)^2\pm k$  

- in front means reflected -opens down
a = vertical stretch or compress
( x + h) shift left or right (opposite of sign)
K is shift up or down + is up, - is down

Multiple Choice

Which quadratic function below is not reflected down?

• $f\left(x\right)=-\frac{1}{2}\left(x+3\right)^2+4$

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

• $f\left(x\right)=-x^2-4$

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

Multiple Choice

Match the description to its equation.
Moves down 1
Moves right 1

• A
• B
• C
• D

Multiple Choice

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

Multiple Choice

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

Multiple Choice

Match the description to its equation.
- moves down 3

• A
• B
• C
• D

Multiple Choice

Match the description to its equation.
Moves right 7

• A
• B
• C
• D

Multiple Choice

Match the description to its equation.
Moves up 2
Moves left 4

• A
• B
• C
• D

Multiple Choice

Match the description to its equation.
Reflected over the x-axis 
Stretched by a factor of 2

• A
• B
• C
• D

Multiple Choice

Which transformation maps the graph of

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

• a reflection across the x-axis

• a translation shifting 4 units up.

• a translation shifting 4 units to the left

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