Chapter 9.1, Problem 14P

Graph each functions.

$f(x)=-\frac{1}{2}{x}^2+5$

To determine

To sketch the given function $f\left(x\right)=-\frac{1}{2}{x}^2+5$ .

Explanation of Solution

Given information:

The given is $f\left(x\right)=-\frac{1}{2}{x}^2+5$ .

Graph:

  

Interpretation:

Let the given equation be $f\left(x\right)=y=-\frac{1}{2}{x}^2+5$

Here the equation is rearranged as $y-5=-\frac{1}{2}{x}^2$

$x$	$-\frac{1}{2}{x}^2+5$
$-2$	$3$
$-1$	$4.5$
$0$	$5$
$1$	$4.5$
$2$	$3$

Using the above table, the graph can be plotted. Thus the origin shifts from $\left(0,0\right)$ to $\left(0,5\right)$ .

The nature of the graph is same as $y=-a{x}^2$ .

Therefore, we have sketched the graph of $f\left(x\right)=-\frac{1}{2}{x}^2+5$ .