Quadratic Transformations

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 following quadratic up 3 units?

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

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

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

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

•  $f\left(x\right)=\left(x-7\right)^2$  

What is the vertex?

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

• (-2,5)

• (2,5)

• (2,-5)

• (-2,-5)

Which equation would shift the quadratic equation right 3?

 $f\left(x\right)=2\left(x+1\right)^2+6$  

•  $f\left(x\right)=2\left(x-3\right)^2+6$  
  

•  $f\left(x\right)=2\left(x-2\right)^2+6$  

•  $f\left(x\right)=2\left(x+1\right)^2+9$  
  

•  $f\left(x\right)=2\left(x+4\right)^2+6$  

What is the new equation of the quadratic below that has a vertical shift of 4 units?

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

•  $f\left(x\right)=-\left(x+6\right)^2-5$  

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

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

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

What is the vertex?

 $f\left(x\right)=2\left(x+1\right)^2+6$  

• (-1, 6)

• (2, 1)

• (1, 6)

• (6, -1)

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 equation would shift the quadratic function

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

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

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

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

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

Which equation would vertically stretch the quadratic function

 $f\left(x\right)=x^2$  by a factor of 3 and shift it 4 to the right?

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

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

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

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

Which quadratic function below is not reflected down?

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

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

• $f\left(x\right)=-x^2-4$

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