Figure

Use transformations to graph the function $f( x) = ( x+3) ^{2}-5$ .

Graph $f$ in steps:

Observe that

$f$ is basically a square function, so begin by graphing

$y=x^{2}$ in Figure 43(a).

Replace the argument

$x$ with

$x+3$ to obtain

$y=( x+3) ^{2}$ . This shifts the graph of

$f$ horizontally to the left

$3$ units, as shown in Figure 43(b).

Finally, subtract

$5$ from each

$y$ -coordinate, which shifts the graph in Figure 42(b) vertically down

$5$ units, and results in the graph of

$f( x) =( x+3) ^{2}-5$ shown in Figure 43(c).