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

$y^{2} = x + 64$

Step 1

Find the x-intercepts.

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

${(0)}^{2} = x + 64$

Solve the equation.

Rewrite the equation as $x + 64 = {(0)}^{2}$ .

$x + 64 = {(0)}^{2}$

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

$x + 64 = 0$

Subtract $64$ from both sides of the equation.

$x = - 64$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Add $0$ and $64$ .

$y^{2} = 64$

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

$y = \pm \sqrt{64}$

Simplify $\pm \sqrt{64}$ .

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

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

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

$y = \pm 8$

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.

$y = 8$

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

$y = - 8$

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

$y = 8, - 8$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4