Find the x and y Intercepts f(x)=(x^3)/(2x^2-8)

$f (x) = \frac{x^{3}}{2 x^{2} - 8}$

Find the x-intercepts.

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

$0 = \frac{x^{3}}{2 x^{2} - 8}$

Solve the equation.

Set the numerator equal to zero.

$x^{3} = 0$

Solve the equation for $x$ .

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

$x = \sqrt[3]{0}$

Simplify $\sqrt[3]{0}$ .

Rewrite $0$ as $0^{3}$ .

$x = \sqrt[3]{0^{3}}$

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

$x = 0$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = \frac{{(0)}^{3}}{2 {(0)}^{2} - 8}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{3}}{2 {(0)}^{2} - 8}$

Remove parentheses.

$y = \frac{0^{3}}{2 \cdot 0^{2} - 8}$

Remove parentheses.

$y = \frac{{(0)}^{3}}{2 {(0)}^{2} - 8}$

Simplify $\frac{{(0)}^{3}}{2 {(0)}^{2} - 8}$ .

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

$y = \frac{0}{2 \cdot 0^{2} - 8}$

Simplify the denominator.

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

$y = \frac{0}{2 \cdot 0 - 8}$

Multiply $2$ by $0$ .

$y = \frac{0}{0 - 8}$

Subtract $8$ from $0$ .

$y = \frac{0}{- 8}$

Divide $0$ by $- 8$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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