### Home > CCA2 > Chapter C > Lesson C.1.2 > ProblemC-28

C-28.

Given the quadratic function $f(x) = x^2 - 3$, find the new expression for each part below and describe the transformation. C-28 HW eTool (Desmos). Homework 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).