Find the x and y Intercepts g(x)=-x(x+6)

$g (x) = - x (x + 6)$

Find the x-intercepts.

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

$0 = - x (x + 6)$

Solve the equation.

Rewrite the equation as $- x (x + 6) = 0$ .

$- x (x + 6) = 0$

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

$x = 0$

$x + 6 = 0$

Set $x$ equal to $0$ .

$x = 0$

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

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

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

The final solution is all the values that make $- x (x + 6) = 0$ true.

$x = 0, - 6$

x-intercept(s) in point form.

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

Find the y-intercepts.

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

$y = 0 ((0) + 6)$

Solve the equation.

Remove parentheses.

$y = 0 (0 + 6)$

Remove parentheses.

$y = 0 ((0) + 6)$

Simplify $0 ((0) + 6)$ .

Add $0$ and $6$ .

$y = 0 \cdot 6$

Multiply $0$ by $6$ .

$y = 0$

y-intercept(s) in point form.

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

List the intersections.

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

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