Transformations of Quadratic Functions

State the vertex of the function.

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

• (3, -5)

• (-3, -5)

• (-3, 5)

• (3, 5)

State the vertex of the function.

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

• (-4, -1)

• (4, 1)

• (-4, 1)

• (4, -1)

State the vertex of the function.

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

• (5, 2)

• (-5, 2)

• (5, -2)

• (-5, -2)

State the transformations of the function.

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

• reflected across the x-axis, shifted left 3, and up 2

• shifted right 3 and up 2

• shifted left 3 and up 2

• shifted up 3 and left 2

State all the transformations of the function.

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

• reflected across the x-axis, shifted left 1, and up 4

• shifted right 1 and up 4

• stretched, shifted left 1, and down 4

• reflected across the x-axis, shifted right 1, and up 4

State all the transformations of the function.

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

• stretched by 1/3 and shifted right 2

• reflected across the x-axis and shifted down 2

• compressed by 1/3 and shifted right 2

• compressed by 1/3 and shifted up 2

Which equation has the transformations for

 $f\left(x\right)=x^2$  
shifted left 5 and up 4

•  $f\left(x\right)=\left(x+5\right)^2+4$  

•  $f\left(x\right)=\left(x-5\right)^2+4$  

•  $f\left(x\right)=\left(x-5\right)^2-4$  

•  $f\left(x\right)=\left(x+5\right)^2-4$  

Which equation has the transformations for
 $f\left(x\right)=x^2$  
stretched by a factor of 3, shifted up 2, and left 1

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

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

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

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

Which equation has the transformations for
 $f\left(x\right)=x^2$  
reflected across the x-axis and shifted right 4

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

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

•  $f\left(x\right)=-x^2+4$  

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

Which of the following graphs matches the equation? 

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

• 
• 
• 
•