Find the x and y Intercepts y=-x^2-6x

$y = - x^{2} - 6 x$

Step 1

Find the x-intercepts.

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

$0 = - x^{2} - 6 x$

Solve the equation.

Rewrite the equation as $- x^{2} - 6 x = 0$ .

$- x^{2} - 6 x = 0$

Factor $- x$ out of $- x^{2} - 6 x$ .

Factor $- x$ out of $- x^{2}$ .

$- x \cdot x - 6 x = 0$

Factor $- x$ out of $- 6 x$ .

$- x \cdot x - x \cdot 6 = 0$

Factor $- x$ out of $- x (x) - x (6)$ .

$- x (x + 6) = 0$

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): $(0, 0), (- 6, 0)$

Step 2

Find the y-intercepts.

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

$y = - {(0)}^{2} - 6 \cdot 0$

Solve the equation.

Remove parentheses.

$y = - 0^{2} - 6 \cdot 0$

Remove parentheses.

$y = - {(0)}^{2} - 6 \cdot 0$

Simplify $- {(0)}^{2} - 6 \cdot 0$ .

Simplify each term.

Raising $0$ to any positive power yields $0$ .

$y = - 0 - 6 \cdot 0$

Multiply $- 1$ by $0$ .

$y = 0 - 6 \cdot 0$

Multiply $- 6$ by $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

y-intercept(s) in point form.

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

Step 3

List the intersections.

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

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

Step 4

Find the x and y Intercepts y=-x^2-6x

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