Find the x and y Intercepts y^2-x-25=0

$y^{2} - x - 25 = 0$

Step 1

Find the x-intercepts.

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

${(0)}^{2} - x - 25 = 0$

Solve the equation.

Simplify ${(0)}^{2} - x - 25$ .

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

$0 - x - 25 = 0$

Subtract $x$ from $0$ .

$- x - 25 = 0$

Add $25$ to both sides of the equation.

$- x = 25$

Divide each term in $- x = 25$ by $- 1$ and simplify.

Divide each term in $- x = 25$ by $- 1$ .

$\frac{- x}{- 1} = \frac{25}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{25}{- 1}$

Divide $x$ by $1$ .

$x = \frac{25}{- 1}$

Simplify the right side.

Divide $25$ by $- 1$ .

$x = - 25$

x-intercept(s) in point form.

x-intercept(s): $(- 25, 0)$

Step 2

Find the y-intercepts.

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

$y^{2} - (0) - 25 = 0$

Solve the equation.

Simplify $y^{2} - (0) - 25$ .

Multiply $- 1$ by $0$ .

$y^{2} + 0 - 25 = 0$

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

$y^{2} - 25 = 0$

Add $25$ to both sides of the equation.

$y^{2} = 25$

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

$y = \pm \sqrt{25}$

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$y = \pm \sqrt{5^{2}}$

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

$y = \pm 5$

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.

$y = 5$

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

$y = - 5$

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

$y = 5, - 5$

y-intercept(s) in point form.

y-intercept(s): $(0, 5), (0, - 5)$

Step 3

List the intersections.

x-intercept(s): $(- 25, 0)$

y-intercept(s): $(0, 5), (0, - 5)$

Step 4

Find the x and y Intercepts y^2-x-25=0

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