Find the x and y Intercepts P(x)=(x-2)^2(x-6)

$P (x) = {(x - 2)}^{2} (x - 6)$

Find the x-intercepts.

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

$0 = {(x - 2)}^{2} (x - 6)$

Solve the equation.

Rewrite the equation as ${(x - 2)}^{2} (x - 6) = 0$ .

${(x - 2)}^{2} (x - 6) = 0$

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

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

$x - 6 = 0$

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 $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Set $x - 6$ equal to $0$ and solve for $x$ .

Set $x - 6$ equal to $0$ .

$x - 6 = 0$

Add $6$ to both sides of the equation.

$x = 6$

The final solution is all the values that make ${(x - 2)}^{2} (x - 6) = 0$ true.

$x = 2, 6$

x-intercept(s) in point form.

x-intercept(s): $(2, 0), (6, 0)$

Find the y-intercepts.

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

$y = {((0) - 2)}^{2} ((0) - 6)$

Solve the equation.

Remove parentheses.

$y = {(0 - 2)}^{2} ((0) - 6)$

Remove parentheses.

$y = {(0 - 2)}^{2} (0 - 6)$

Remove parentheses.

$y = {((0) - 2)}^{2} ((0) - 6)$

Simplify ${((0) - 2)}^{2} ((0) - 6)$ .

Subtract $2$ from $0$ .

$y = {(- 2)}^{2} ((0) - 6)$

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

$y = 4 ((0) - 6)$

Subtract $6$ from $0$ .

$y = 4 \cdot - 6$

Multiply $4$ by $- 6$ .

$y = - 24$

y-intercept(s) in point form.

y-intercept(s): $(0, - 24)$

List the intersections.

x-intercept(s): $(2, 0), (6, 0)$

y-intercept(s): $(0, - 24)$

Find the x and y Intercepts P(x)=(x-2)^2(x-6)

Related Questions

Support LCMGCF.com by disabling your adblocker.