Find the x and y Intercepts y^2-x-36=0

$y^{2} - x - 36 = 0$

Step 1

Find the x-intercepts.

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

${(0)}^{2} - x - 36 = 0$

Solve the equation.

Simplify ${(0)}^{2} - x - 36$ .

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

$0 - x - 36 = 0$

Subtract $x$ from $0$ .

$- x - 36 = 0$

Add $36$ to both sides of the equation.

$- x = 36$

Divide each term in $- x = 36$ by $- 1$ and simplify.

Divide each term in $- x = 36$ by $- 1$ .

$\frac{- x}{- 1} = \frac{36}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{36}{- 1}$

Divide $x$ by $1$ .

$x = \frac{36}{- 1}$

Simplify the right side.

Divide $36$ by $- 1$ .

$x = - 36$

x-intercept(s) in point form.

x-intercept(s): $(- 36, 0)$

Step 2

Find the y-intercepts.

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

$y^{2} - (0) - 36 = 0$

Solve the equation.

Simplify $y^{2} - (0) - 36$ .

Multiply $- 1$ by $0$ .

$y^{2} + 0 - 36 = 0$

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

$y^{2} - 36 = 0$

Add $36$ to both sides of the equation.

$y^{2} = 36$

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

$y = \pm \sqrt{36}$

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$y = \pm \sqrt{6^{2}}$

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

$y = \pm 6$

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.

$y = 6$

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

$y = - 6$

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

$y = 6, - 6$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(- 36, 0)$

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

Step 4

Find the x and y Intercepts y^2-x-36=0

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