### Home > CCA > Chapter 11 > Lesson 11.2.2 > Problem 11-48

11-48.

Given the quadratic function

*f*(*x*) =*x*^{2}− 3, find the new expression for each part below and describe the transformation.*11-48 HW eTool*(Desmos). Homework Help ✎*f*(*x*) − 2−2 ·

*f*(*x*)*f*(*x*− 2)*f*(−2*x*)

See problems 11−10 and 11−22 for additional help.

Substitute *x*^{2} − 3 for *f*(*x*).*f*(*x*) − 2

(*x*^{2} − 3) − 2

What effect will that have on the graph?

*x*^{2} − 5

See the help for part (a).

Reflected over *x*-axis, stretched.

Substitute (*x* − 2) for *x* in *x*^{2} −3.*f*(*x*) = *x*^{2} − 3*f*(*x* − 2) = (*x* − 2)^{2} − 3

Shifted right 2 units.

See help for part (c).

Use the eTool below to help you explore the transformations.

Click on the link at right for the full eTool version: CCA 11-48 HW eTool