Find the x and y Intercepts f(x)=x(x^2-6)

$f (x) = x (x^{2} - 6)$

Find the x-intercepts.

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

$0 = x (x^{2} - 6)$

Solve the equation.

Rewrite the equation as $x (x^{2} - 6) = 0$ .

$x (x^{2} - 6) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x^{2} - 6 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x^{2} - 6$ equal to $0$ and solve for $x$ .

Set $x^{2} - 6$ equal to $0$ .

$x^{2} - 6 = 0$

Solve $x^{2} - 6 = 0$ for $x$ .

Add $6$ to both sides of the equation.

$x^{2} = 6$

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

$x = \pm \sqrt{6}$

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.

$x = \sqrt{6}$

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

$x = - \sqrt{6}$

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

$x = \sqrt{6}, - \sqrt{6}$

The final solution is all the values that make $x (x^{2} - 6) = 0$ true.

$x = 0, \sqrt{6}, - \sqrt{6}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (\sqrt{6}, 0), (- \sqrt{6}, 0)$

Find the y-intercepts.

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

$y = (0) ({(0)}^{2} - 6)$

Solve the equation.

Remove parentheses.

$y = 0 (0^{2} - 6)$

Remove parentheses.

$y = (0) ({(0)}^{2} - 6)$

Simplify $(0) ({(0)}^{2} - 6)$ .

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

$y = 0 (0 - 6)$

Subtract $6$ from $0$ .

$y = 0 \cdot - 6$

Multiply $0$ by $- 6$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0, 0), (\sqrt{6}, 0), (- \sqrt{6}, 0)$

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

Find the x and y Intercepts f(x)=x(x^2-6)

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