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

$f (x) = 2 x (x + 3)$

Find the x-intercepts.

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

$0 = 2 x (x + 3)$

Solve the equation.

Rewrite the equation as $2 x (x + 3) = 0$ .

$2 x (x + 3) = 0$

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

$x = 0$

$x + 3 = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ 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 $2 x (x + 3) = 0$ true.

$x = 0, - 3$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = 2 (0) ((0) + 3)$

Solve the equation.

Remove parentheses.

$y = 2 (0) (0 + 3)$

Remove parentheses.

$y = 2 (0) ((0) + 3)$

Simplify $2 (0) ((0) + 3)$ .

Multiply $2$ by $0$ .

$y = 0 ((0) + 3)$

Add $0$ and $3$ .

$y = 0 \cdot 3$

Multiply $0$ by $3$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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