### Home > CCAA8 > Chapter 11 Unit 12 > Lesson CCA: 11.2.2 > Problem11-48

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).

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

1. $f(x)−2$

Substitute $x^2−3$ for $f(x)$.
$f(x)−2$
$(x^2−3)−2$
What effect will that have on the graph?

$x^2−5$

1. $−2·f(x)$

See the help for part (a).

Reflected over $x$-axis, stretched.

1. $f(x−2)$

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.

1. $f(−2x)$

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