Chapter 4.4, Problem 4LC

To determine

To graph: The equation $y=-x^2+2$ on the graph paper.

Explanation of Solution

Given:

The equation is $y=-x^2+2$ .

Calculation:

Substitute $x=0$ in the given equation to obtain the value of $y$ as follows:

  $\begin{array}{c}y=-0^2+2\\ =0+2\\ =2\end{array}$

Substitute $x=1$ in the given equation to obtain the value of $y$ as follows:

  $\begin{array}{c}y=-1^2+2\\ =-1+2\\ =1\end{array}$

Substitute $x=2$ in the given equation to obtain the value of $y$ as follows:

  $\begin{array}{c}y=-2^2+2\\ =-4+2\\ =-2\end{array}$

Substitute $y=0$ in the given equation to obtain the value of $x$ as follows:

  $\begin{array}{c}0=-x^2+2\\ 2=x^2\\ x=\pm \sqrt{2}\end{array}$

Substitute the obtained values in the table given below.

$x$	$y$
0	2
1	1
2	$-2$
$\pm \sqrt{2}$	0

Plot the points and join them to obtain the graph as follows: