Find the x and y Intercepts y=(x-2)^3(x+3)^2

$y = {(x - 2)}^{3} {(x + 3)}^{2}$

Step 1

Find the x-intercepts.

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

$0 = {(x - 2)}^{3} {(x + 3)}^{2}$

Solve the equation.

Rewrite the equation as ${(x - 2)}^{3} {(x + 3)}^{2} = 0$ .

${(x - 2)}^{3} {(x + 3)}^{2} = 0$

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

${(x - 2)}^{3} = 0$

${(x + 3)}^{2} = 0$

Set ${(x - 2)}^{3}$ equal to $0$ and solve for $x$ .

Set ${(x - 2)}^{3}$ equal to $0$ .

${(x - 2)}^{3} = 0$

Solve ${(x - 2)}^{3} = 0$ for $x$ .

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set ${(x + 3)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x + 3)}^{2}$ equal to $0$ .

${(x + 3)}^{2} = 0$

Solve ${(x + 3)}^{2} = 0$ for $x$ .

Set the $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make ${(x - 2)}^{3} {(x + 3)}^{2} = 0$ true.

$x = 2, - 3$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (- 3, 0)$

Step 2

Find the y-intercepts.

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

$y = {((0) - 2)}^{3} {((0) + 3)}^{2}$

Solve the equation.

Remove parentheses.

$y = {(0 - 2)}^{3} {((0) + 3)}^{2}$

Remove parentheses.

$y = {(0 - 2)}^{3} {(0 + 3)}^{2}$

Remove parentheses.

$y = {((0) - 2)}^{3} {((0) + 3)}^{2}$

Simplify ${((0) - 2)}^{3} {((0) + 3)}^{2}$ .

Subtract $2$ from $0$ .

$y = {(- 2)}^{3} {((0) + 3)}^{2}$

Raise $- 2$ to the power of $3$ .

$y = - 8 {((0) + 3)}^{2}$

Add $0$ and $3$ .

$y = - 8 \cdot 3^{2}$

Raise $3$ to the power of $2$ .

$y = - 8 \cdot 9$

Multiply $- 8$ by $9$ .

$y = - 72$

y-intercept(s) in point form.

y-intercept(s): $(0, - 72)$

Step 3

List the intersections.

x-intercept(s): $(2, 0), (- 3, 0)$

y-intercept(s): $(0, - 72)$

Step 4

Find the x and y Intercepts y=(x-2)^3(x+3)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.