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

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

Step 1

Find the x-intercepts.

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

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

Solve the equation.

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

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

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

$x = 0$

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

Set $x$ equal to $0$ .

$x = 0$

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 $0$ .

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

$x = 0, 3$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Subtract $3$ from $0$ .

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

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

$y = 0 \cdot 9$

Multiply $0$ by $9$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

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

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