Quadratic Transformations S25

What is the vertex?

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

• (-4,3)

• (4,3)

• (-4,-3)

• (4,-3)

Which equation would shift the quadratic function

 $f\left(x\right)=x^2$  up 3 units and to the right 4 units.

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

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

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

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

Which quadratic function below is not reflected down?

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

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

• $f\left(x\right)=-x^2-4$

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

Describe the transformation:

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

• right 3, down 2

• up 3, left 2

• left 3, up 2

• left 3, down 2

Describe the transformation:

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

• right 3

• Reflected down, right 3

• Reflected down, up 3

• Reflected down, left 3

Which equation matches the following transformation: up 4, stretched 3, reflected down, and left 1

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

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

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

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

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

Match the equation to its description.

• Vertically stretched by 2 and shifted up 4

• Vertically compressed by 2 and shifted up 4

• Vertically stretched by 2 and shifted left 4

• Vertically compressed by 2 and shifted left 4

Match the equation to its description.

• Reflected over x-axis and shifted up 4

• Reflected over x-axis and shifted down 4

• Reflected over x-axis and shifted right 4

• Reflected over x-axis and shifted left 4