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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$x = 0$

$x - 2 = 0$

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

Set $x$ equal to $0$ .

$x = 0$

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

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set ${(x + 1)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x + 1)}^{2}$ equal to $0$ .

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

Solve ${(x + 1)}^{2} = 0$ for $x$ .

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

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

$x = 0, 2, - 1$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $2$ from $0$ .

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

Multiply $0$ by $- 2$ .

$y = 0 {((0) + 1)}^{2}$

Add $0$ and $1$ .

$y = 0 \cdot 1^{2}$

One to any power is one.

$y = 0 \cdot 1$

Multiply $0$ by $1$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

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

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