Quadratic Transformations

What is the vertex?

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

• (-4,3)

• (4,3)

• (-4,-3)

• (4,-3)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Which equation would shift the quadratic function

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

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

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

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

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

Which equation would shift the quadratic function

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

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

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

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

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

Tags

CCSS.HSF.BF.B.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?

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

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

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

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

Tags

CCSS.HSF.BF.B.3

Which quadratic function below is not reflected down?

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

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

• $f\left(x\right)=-x^2-4$

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

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

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

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

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

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

Write an equation of a quadratic that is translated down 2 units.

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

• $f\left(x\right)=x^2-2$

• $f\left(x\right)=-x^2+2$

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

Which quadratic would be the narrowest?

• $f\left(x\right)=\frac{1}{2}x^2$

• $f\left(x\right)=x^2$

• $f\left(x\right)=3x^2$

• $f\left(x\right)=5x^2$

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7