Chapter 9.1, Problem 13P

Graph each functions.

$f(x)=2x^2+1$

To determine

To sketch the given function $f\left(x\right)=2x^2+1$ .

Explanation of Solution

Given information:

The given is $f\left(x\right)=2x^2+1$ .

Graph:

  

Interpretation:

Let the given equation be $f\left(x\right)=y=2x^2+1$

Here the equation is rearranged as $y-1=2x^2$

$x$	$2x^2+1$
$-2$	$9$
$-1$	$3$
$0$	$1$
$1$	$3$
$2$	$9$

Using the above table, the graph can be plotted. Thus the origin shifts from $\left(0,0\right)$ to $\left(0,1\right)$ .

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

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