Find the x and y Intercepts x^2+y-64=0

$x^{2} + y - 64 = 0$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$x^{2} + 0 - 64 = 0$

Solve the equation.

Add $x^{2}$ and $0$ .

$x^{2} - 64 = 0$

Add $64$ to both sides of the equation.

$x^{2} = 64$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$x = \pm \sqrt{8^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 8$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 8$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 8$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 8, - 8$

x-intercept(s) in point form.

x-intercept(s): $(8, 0), (- 8, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

${(0)}^{2} + y - 64 = 0$

Solve the equation.

Simplify ${(0)}^{2} + y - 64$ .

Raising $0$ to any positive power yields $0$ .

$0 + y - 64 = 0$

Add $0$ and $y$ .

$y - 64 = 0$

Add $64$ to both sides of the equation.

$y = 64$

y-intercept(s) in point form.

y-intercept(s): $(0, 64)$

Step 3

List the intersections.

x-intercept(s): $(8, 0), (- 8, 0)$

y-intercept(s): $(0, 64)$

Step 4