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

$x^{2} (x - 6) (x + 6)$

Step 1

Write $x^{2} (x - 6) (x + 6)$ as an equation.

$y = x^{2} (x - 6) (x + 6)$

Step 2

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$x^{2} = 0$

$x - 6 = 0$

$x + 6 = 0$

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

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

$x^{2} = 0$

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

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

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

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

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

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

$x = 0, 6, - 6$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (6, 0), (- 6, 0)$

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

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

$y = 0 ((0) - 6) ((0) + 6)$

Subtract $6$ from $0$ .

$y = 0 \cdot - 6 ((0) + 6)$

Multiply $0$ by $- 6$ .

$y = 0 ((0) + 6)$

Add $0$ and $6$ .

$y = 0 \cdot 6$

Multiply $0$ by $6$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(0, 0), (6, 0), (- 6, 0)$

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

Step 5

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

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