Question

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

$y=-x^2+4.$

Short answer

The intercepts are :

x-intercepts a$\left(-2,0\right)$and $\left(2,0\right)$,

y-intercept is$\left(0,4\right)$.

Step-by-step solution

Given information:

Consider the equation,

$y=-x^2+4$.

To find the x-intercept:

Let $y=0$in the equation,

Then, $-x^2+4=0$

$\left(-1\right)\times \left(-x^2+4\right)=\left(-1\right)\times 0$ [Multiply by $\left(-1\right)$on both sides.]

$x^2-4=0$

$\left(x+2\right)\left(x-2\right)=0$ [Factors]

$x+2=0$ or $x-2=0$ [Zero Product Property]

$x=-2$ or $x=2$

The equation has two solutions, $-2and2.$

$x-interceptsare\left(-2,0\right)and\left(2,0\right).$

To find the y-intercept:

Let $x=0$in the equation,

Then, $y=0+4$

$y=4$

$y-interceptis\left(0,4\right).$

To draw the graph:

We can draw the graph of the equation $y=-x^2+4$by plotting the above intercepts and the points in the table below,

$x$	$y=-x^2+4$	$\left(x,y\right)$
$-3$	$-5$	$\left(-3,-5\right)$
$-1$	$3$	$\left(-1,3\right)$
$1$	$3$	$\left(1,3\right)$
$3$	$-5$