Find the x and y Intercepts f(x)=(x^2+25)

$f (x) = (x^{2} + 25)$

Find the x-intercepts.

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

$0 = x^{2} + 25$

Solve the equation.

Rewrite the equation as $x^{2} + 25 = 0$ .

$x^{2} + 25 = 0$

Subtract $25$ from both sides of the equation.

$x^{2} = - 25$

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

$x = \pm \sqrt{- 25}$

Simplify $\pm \sqrt{- 25}$ .

Rewrite $- 25$ as $- 1 (25)$ .

$x = \pm \sqrt{- 1 (25)}$

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{25}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \cdot \sqrt{25}$

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

$x = \pm i \cdot \sqrt{5^{2}}$

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

$x = \pm i \cdot 5$

Move $5$ to the left of $i$ .

$x = \pm 5 i$

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.

$x = 5 i$

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

$x = - 5 i$

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

$x = 5 i, - 5 i$

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

x-intercept(s): $None$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

$y = 0^{2} + 25$

Remove parentheses.

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

Simplify ${(0)}^{2} + 25$ .

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

$y = 0 + 25$

Add $0$ and $25$ .

$y = 25$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $None$

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

Find the x and y Intercepts f(x)=(x^2+25)

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