Chapter 8.2, Problem 3E

To determine

To graph:Graph the function. Compare the graph to the graph of $f(x)=x^2$.

Answer to Problem 3E

Graph:

  

Here, both the graphs open up and have the same axis of symmetry $x=0$ . The vertex of $g$ is $(0,6)$ which is above the vertex of $f$ , $(0,0)$ . The graph of $g$ is shifted by $6$ units up of the graph of $f$.

Explanation of Solution

Giveninformation:

The function is $g(x)=x^2+6$.

Graph:

To graph the function, let’s make the table values as follows:

$x$	$-2$	$-1$	0	1	2
$g(x)$	10	7	6	7	10

Now, plotting the ordered pairs and drawing a smooth curve through the points, we get the following graph.

  

Interpretation:

Here, both the graphs open up and have the same axis of symmetry $x=0$ . The vertex of $g$ is $(0,6)$ which is above the vertex of $f$ , $(0,0)$ . The graph of $g$ is shifted by $6$ units up of the graph of $f$.