Q. 16 - Precalculus Enhanced with Graphing Utilities

Question

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts.

$y=x^2-9$.

Step-by-Step Solution

Answer

The intercepts are :

x-intercepts are$\left(-3,0\right) and (3,0)$ ,

y-intercept is  $\left(0,-9\right)$.

Step 1: Given information:

Consider the equation,

$y=x^2-9$.

Step 2: To find the x-intercept:

Let $y=0$ in the equation,

 Then $x^2-9=0$

$\left(x+3\right)\left(x-3\right)=0$ [Factors]

$x+3=0$ or $x-3=0$ [Zero Product Property]

$x=-3$ or $x=3$

The equation has two solution, $-3 and 3.$

$x-intercepts are \left(-3,0\right) and \left(3,0\right).$

Step 3: To find the y-intercept:

Let $x=0$ in the equation,

Then, $y=0-9$

$y=-9$.

$y-intercept is \left(0,-9\right)$.

Step 4: To draw the graph:

We can draw the graph of the equation $y=x^2-9$ by plotting the above intercepts and the points in the table below,

x	$y=x^2-9$	$\left(x,y\right)$
-2	-5	$\left(-2,-5\right)$
-1	-8	$\left(-1,-8\right)$
1	-8	$\left(1,-8\right)$
2	-5	$\left(2,-5\right)$