Find the x and y Intercepts y^2=x+121

$y^{2} = x + 121$

Step 1

Find the x-intercepts.

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

${(0)}^{2} = x + 121$

Solve the equation.

Rewrite the equation as $x + 121 = {(0)}^{2}$ .

$x + 121 = {(0)}^{2}$

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

$x + 121 = 0$

Subtract $121$ from both sides of the equation.

$x = - 121$

x-intercept(s) in point form.

x-intercept(s): $(- 121, 0)$

Step 2

Find the y-intercepts.

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

$y^{2} = (0) + 121$

Solve the equation.

Add $0$ and $121$ .

$y^{2} = 121$

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

$y = \pm \sqrt{121}$

Simplify $\pm \sqrt{121}$ .

Rewrite $121$ as $11^{2}$ .

$y = \pm \sqrt{11^{2}}$

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

$y = \pm 11$

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.

$y = 11$

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

$y = - 11$

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

$y = 11, - 11$

y-intercept(s) in point form.

y-intercept(s): $(0, 11), (0, - 11)$

Step 3

List the intersections.

x-intercept(s): $(- 121, 0)$

y-intercept(s): $(0, 11), (0, - 11)$

Step 4