Find the x and y Intercepts f(x)=-2x(x^2-1)

$f (x) = - 2 x (x^{2} - 1)$

Step 1

Find the x-intercepts.

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

$0 = - 2 x (x^{2} - 1)$

Solve the equation.

Rewrite the equation as $- 2 x (x^{2} - 1) = 0$ .

$- 2 x (x^{2} - 1) = 0$

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

$x = 0$

$x^{2} - 1 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x^{2} - 1$ equal to $0$ and solve for $x$ .

Set $x^{2} - 1$ equal to $0$ .

$x^{2} - 1 = 0$

Solve $x^{2} - 1 = 0$ for $x$ .

Add $1$ to both sides of the equation.

$x^{2} = 1$

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

$x = \pm \sqrt{1}$

Any root of $1$ is $1$ .

$x = \pm 1$

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.

$x = 1$

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

$x = - 1$

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

$x = 1, - 1$

The final solution is all the values that make $- 2 x (x^{2} - 1) = 0$ true.

$x = 0, 1, - 1$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (1, 0), (- 1, 0)$

Step 2

Find the y-intercepts.

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

$y = - 2 \cdot 0 ({(0)}^{2} - 1)$

Solve the equation.

Remove parentheses.

$y = - 2 \cdot (0 (0^{2} - 1))$

Remove parentheses.

$y = - 2 \cdot (0 ({(0)}^{2} - 1))$

Simplify $- 2 \cdot (0 ({(0)}^{2} - 1))$ .

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

$y = - 2 \cdot (0 (0 - 1))$

Subtract $1$ from $0$ .

$y = - 2 \cdot (0 \cdot - 1)$

Multiply $- 2 (0 \cdot - 1)$ .

Multiply $0$ by $- 1$ .

$y = - 2 \cdot 0$

Multiply $- 2$ by $0$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

x-intercept(s): $(0, 0), (1, 0), (- 1, 0)$

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

Step 4

Find the x and y Intercepts f(x)=-2x(x^2-1)

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