Question

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

$y=x^2-9$.

Short answer

The intercepts are :

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

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

Step-by-step solution

Given information:

Consider the equation,

$y=x^2-9$.

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, $-3and3.$

localid="1646704625840" $x-interceptsare\left(-3,0\right)and\left(3,0\right).$

To find the y-intercept:

Let $x=0$in the equation,

Then, $y=0-9$

$y=-9$.

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

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	$\left(2,-5\right)$