Chapter 8.2, Problem 10E

To determine

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

Answer to Problem 10E

Graph:

  

Here, the graph of $f$ is opened up and that of $t$ is opened down and they both have the same axis of symmetry $x=0$ . The graph of $t$ is a vertical stretch by a factor of 3 units, a reflection about the x -axis and a vertical shift by 1 unit up of the graph of $f$.

Explanation of Solution

Giveninformation:

The function is $t(x)=-3x^2+1$.

Graph:

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

$x$	$-2$	$-1$	0	1	2
$t(x)$	$-11$	$-2$	1	$-2$	$-11$

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

  

Interpretation:

Here, the graph of $f$ is opened up and that of $t$ is opened down and they bothhave the same axis of symmetry $x=0$ . The graph of $t$ is a vertical stretch by a factor of 3 units, a reflection about the x -axis and a vertical shift by 1unitup of the graph of $f$.