### Home > INT2 > Chapter 9 > Lesson 9.3.1 > Problem9-81

9-81.

Given the quadratic function $f(x) = x^2$, write an equation for each transformation below, and describe how the transformed graph would be different from the original graph. .

1. $a(x) = f(x) - 2$

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

$x^2 - 2$

1. $b(x) = -2 · f(x)$

See the help for part (a).

Reflected over $x$-axis, stretched.

1. $c(x) = f(x - 2)$

Substitute $(x - 2)$ for $x$ in $x^2$
$f(x) = x^2$
$f(x - 2) = (x - 2)^2$

Shifted right $2$ units.

1. $d(x) = f(2x)$

See help for part (c).