Find the x and y Intercepts y=x^4-16

$y = x^{4} - 16$

Find the x-intercepts.

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

$0 = x^{4} - 16$

Solve the equation.

Rewrite the equation as $x^{4} - 16 = 0$ .

$x^{4} - 16 = 0$

Add $16$ to both sides of the equation.

$x^{4} = 16$

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt[4]{16}$

Simplify $\pm \sqrt[4]{16}$ .

Rewrite $16$ as $2^{4}$ .

$x = \pm \sqrt[4]{2^{4}}$

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

$x = \pm 2$

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.

$x = 2$

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

$x = - 2$

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

$x = 2, - 2$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (- 2, 0)$

Find the y-intercepts.

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

$y = {(0)}^{4} - 16$

Solve the equation.

Remove parentheses.

$y = 0^{4} - 16$

Remove parentheses.

$y = {(0)}^{4} - 16$

Simplify ${(0)}^{4} - 16$ .

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

$y = 0 - 16$

Subtract $16$ from $0$ .

$y = - 16$

y-intercept(s) in point form.

y-intercept(s): $(0, - 16)$

List the intersections.

x-intercept(s): $(2, 0), (- 2, 0)$

y-intercept(s): $(0, - 16)$