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

$f (x) = - 2 x (x + 1) (x + 2)$

Step 1

Find the x-intercepts.

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

$0 = - 2 x (x + 1) (x + 2)$

Solve the equation.

Rewrite the equation as $- 2 x (x + 1) (x + 2) = 0$ .

$- 2 x (x + 1) (x + 2) = 0$

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

$x = 0$

$x + 1 = 0$

$x + 2 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 1$ equal to $0$ and solve for $x$ .

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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

$x = 0, - 1, - 2$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (- 1, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

Simplify $- 2 \cdot (0 ((0) + 1) ((0) + 2))$ .

Add $0$ and $1$ .

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

Multiply $0$ by $1$ .

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

Add $0$ and $2$ .

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

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

Multiply $0$ by $2$ .

$y = - 2 \cdot 0$

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): $(0, 0), (- 1, 0), (- 2, 0)$

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

Step 4

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

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