Find the x and y Intercepts y=x(x-2)

$y = x (x - 2)$

Step 1

Find the x-intercepts.

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

$0 = x (x - 2)$

Solve the equation.

Rewrite the equation as $x (x - 2) = 0$ .

$x (x - 2) = 0$

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

$x = 0$

$x - 2 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x - 2$ equal to $0$ and solve for $x$ .

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

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

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

$x = 0, 2$

x-intercept(s) in point form.

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

Step 2

Find the y-intercepts.

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

$y = (0) ((0) - 2)$

Solve the equation.

Remove parentheses.

$y = 0 (0 - 2)$

Remove parentheses.

$y = (0) ((0) - 2)$

Simplify $(0) ((0) - 2)$ .

Subtract $2$ from $0$ .

$y = 0 \cdot - 2$

Multiply $0$ by $- 2$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4