Chapter 1, Problem 17RE

To determine

To find:The graph of the given equation.

Answer to Problem 17RE

The graph of the given equation is shown in Figure-1.

Explanation of Solution

Given information:

Theequation is $y=5-x^2$ .

Calculation:

Consider the equation.

  $y=5-x^2$

Substitute $y=0$ in above equation.

  $\begin{array}{l}0=5-x^2\\ x=\pm \sqrt{5}\end{array}$

Substitute $x=0$ in above equation.

  $\begin{array}{l}y=5-0^2\\ y=5\end{array}$

The intercepts are $\left(\sqrt{5},0\right),\left(-\sqrt{5},0\right),\left(0,5\right)$

For symmetry about $y$ axis substitute $x=-x$ , then we get $y=5-x^2$ .

For symmetry about $x$ axis substitute $y=-y$ , then we get $-y=5-x^2$ .

For symmetry about the origin substitute $x=-x,y=-y$ , then we get $-y=5-x^2$ .

Since, y-axis symmetrycondition results in the equivalent equation.

Thus, the equation is symmetric about y axis.

The graph is shown below.

  

Figure-1