Question

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

$y=x^2-1$.

Short answer

The intercepts are :

x-intercepts are$\left(-1,0\right)and\left(1,0\right)$,

y-intercept is$\left(0,-1\right)$.

Step-by-step solution

Given information:

Consider the equation,

$y=x^2-1$.

To find the x-intercept:

Let $y=0$in the equation,

Then, $x^2-1=0$

$\left(x+1\right)\left(x-1\right)=0$ [Factors]

$x+1=0$or $x-1=0$ [Zero Product Property]

$x=-1$or $x=1$

The equation has two solutions, $-1and1$.

localid="1646707871515" $x-interceptsare\left(-1,0\right)and\left(1,0\right).$

To find the y-intercept:

Let $x=0$in the equation,

Then, $y=0-1$

$y=-1$.

$y-interceptis\left(0,-1\right)$

To draw the graph:

We can draw the graph of the equation $y=x^2-1$by plotting the above intercepts and the points in the table below,

x	$y=x^2-1$	$\left(x,y\right)$
-3	8	$\left(-3,8\right)$
-2	3	$\left(-2,3\right)$
2	3	$\left(2,3\right)$
3	8	$\left(3,8\right)$