Find the x and y Intercepts x=y^2-6

$x = y^{2} - 6$

Step 1

Find the x-intercepts.

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

$x = {(0)}^{2} - 6$

Solve the equation.

Remove parentheses.

$x = 0^{2} - 6$

Remove parentheses.

$x = {(0)}^{2} - 6$

Simplify ${(0)}^{2} - 6$ .

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

$x = 0 - 6$

Subtract $6$ from $0$ .

$x = - 6$

x-intercept(s) in point form.

x-intercept(s): $(- 6, 0)$

Step 2

Find the y-intercepts.

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

$0 = y^{2} - 6$

Solve the equation.

Rewrite the equation as $y^{2} - 6 = 0$ .

$y^{2} - 6 = 0$

Add $6$ to both sides of the equation.

$y^{2} = 6$

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

$y = \pm \sqrt{6}$

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.

$y = \sqrt{6}$

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

$y = - \sqrt{6}$

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

$y = \sqrt{6}, - \sqrt{6}$

y-intercept(s) in point form.

y-intercept(s): $(0, \sqrt{6}), (0, - \sqrt{6})$

Step 3

List the intersections.

x-intercept(s): $(- 6, 0)$

y-intercept(s): $(0, \sqrt{6}), (0, - \sqrt{6})$

Step 4