Find the x and y Intercepts (x+4)(x-5)^2

$(x + 4) {(x - 5)}^{2}$

Step 1

Write $(x + 4) {(x - 5)}^{2}$ as an equation.

$y = (x + 4) {(x - 5)}^{2}$

Step 2

Find the x-intercepts.

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

$0 = (x + 4) {(x - 5)}^{2}$

Solve the equation.

Rewrite the equation as $(x + 4) {(x - 5)}^{2} = 0$ .

$(x + 4) {(x - 5)}^{2} = 0$

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

$x + 4 = 0$

${(x - 5)}^{2} = 0$

Set $x + 4$ equal to $0$ and solve for $x$ .

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Subtract $4$ from both sides of the equation.

$x = - 4$

Set ${(x - 5)}^{2}$ equal to $0$ and solve for $x$ .

Set ${(x - 5)}^{2}$ equal to $0$ .

${(x - 5)}^{2} = 0$

Solve ${(x - 5)}^{2} = 0$ for $x$ .

Set the $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

The final solution is all the values that make $(x + 4) {(x - 5)}^{2} = 0$ true.

$x = - 4, 5$

x-intercept(s) in point form.

x-intercept(s): $(- 4, 0), (5, 0)$

Step 3

Find the y-intercepts.

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

$y = ((0) + 4) {((0) - 5)}^{2}$

Solve the equation.

Remove parentheses.

$y = (0 + 4) {((0) - 5)}^{2}$

Remove parentheses.

$y = (0 + 4) {(0 - 5)}^{2}$

Remove parentheses.

$y = ((0) + 4) {((0) - 5)}^{2}$

Simplify $((0) + 4) {((0) - 5)}^{2}$ .

Add $0$ and $4$ .

$y = 4 {((0) - 5)}^{2}$

Subtract $5$ from $0$ .

$y = 4 {(- 5)}^{2}$

Raise $- 5$ to the power of $2$ .

$y = 4 \cdot 25$

Multiply $4$ by $25$ .

$y = 100$

y-intercept(s) in point form.

y-intercept(s): $(0, 100)$

Step 4

List the intersections.

x-intercept(s): $(- 4, 0), (5, 0)$

y-intercept(s): $(0, 100)$

Step 5

Find the x and y Intercepts (x+4)(x-5)^2

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