CPM Homework Help : INT2 Problem 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.

$a(x) = f(x) - 2$
Hint (a):
Substitute $x^2$ for $f(x)$ .
$f(x) - 2$
$(x^2) - 2$
What effect will that have on the graph?
Partial Answer (a):
$x^2 - 2$

$b(x) = -2 · f(x)$
Hint (b):
See the help for part (a).
Answer (b):
Reflected over $x$ -axis, stretched.

$c(x) = f(x - 2)$
Hint (c):
Substitute $(x - 2)$ for $x$ in $x^2$
$f(x) = x^2$
$f(x - 2) = (x - 2)^2$
Partial Answer (c):
Shifted right $2$ units.

$d(x) = f(2x)$
Hint (d):
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: INT2 9-81 HW eTool