Q. 15 - Precalculus Enhanced with Graphing Utilities

Question

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

$y=x^2-1$.

Step-by-Step Solution

Answer

The intercepts are :

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

y-intercept is $\left(0,-1\right)$.

Step 1: Given information:

Consider the equation,

$y=x^2-1$.

Step 2: 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, $-1 and 1$.

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

Step 3: To find the y-intercept:

Let $x=0$ in the equation,

Then, $y=0-1$

$y=-1$.

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

Step 4: 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	$\left(3,8\right)$