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

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

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

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

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

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.

$x = - 1$

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 $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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

$x = - 1, 1$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $0$ and $1$ .

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

One to any power is one.

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

Multiply $- 1$ by $1$ .

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

Subtract $1$ from $0$ .

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

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{2}$ .

Raise $- 1$ to the power of $1$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

$y = {(- 1)}^{3}$

Raise $- 1$ to the power of $3$ .

$y = - 1$

y-intercept(s) in point form.

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

List the intersections.

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

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

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

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