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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

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

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

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

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

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

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

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

$x + 2 = 0$

Subtract $2$ from 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 $0$ .

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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

$x = - 2, 1$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Add $0$ and $2$ .

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

Raise $2$ to the power of $2$ .

$y = - 1 \cdot 4 {((0) - 1)}^{2}$

Multiply $- 1$ by $4$ .

$y = - 4 {((0) - 1)}^{2}$

Subtract $1$ from $0$ .

$y = - 4 {(- 1)}^{2}$

Raise $- 1$ to the power of $2$ .

$y = - 4 \cdot 1$

Multiply $- 4$ by $1$ .

$y = - 4$

y-intercept(s) in point form.

y-intercept(s): $(0, - 4)$

Step 3

List the intersections.

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

y-intercept(s): $(0, - 4)$

Step 4

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

Related Questions

Support LCMGCF.com by disabling your adblocker.