Find the x and y Intercepts f(x)=-6-x^3-9x^2+3x

$f (x) = - 6 - x^{3} - 9 x^{2} + 3 x$

Find the x-intercepts.

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

$0 = - 6 - x^{3} - 9 x^{2} + 3 x$

Solve the equation.

Remove parentheses.

$0 = - 6 - x^{3} - 9 x^{2} + 3 x$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 9.38765153$

x-intercept(s) in point form.

x-intercept(s): $(- 9.38765153, 0)$

Find the y-intercepts.

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

$y = - 6 - {(0)}^{3} - 9 {(0)}^{2} + 3 (0)$

Solve the equation.

Remove parentheses.

$y = - 6 - 0^{3} - 9 {(0)}^{2} + 3 (0)$

Remove parentheses.

$y = - 6 - 0^{3} - 9 \cdot 0^{2} + 3 (0)$

Remove parentheses.

$y = - 6 - {(0)}^{3} - 9 {(0)}^{2} + 3 (0)$

Simplify $- 6 - {(0)}^{3} - 9 {(0)}^{2} + 3 (0)$ .

Simplify each term.

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

$y = - 6 - 0 - 9 {(0)}^{2} + 3 (0)$

Multiply $- 1$ by $0$ .

$y = - 6 + 0 - 9 {(0)}^{2} + 3 (0)$

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

$y = - 6 + 0 - 9 \cdot 0 + 3 (0)$

Multiply $- 9$ by $0$ .

$y = - 6 + 0 + 0 + 3 (0)$

Multiply $3$ by $0$ .

$y = - 6 + 0 + 0 + 0$

Simplify by adding numbers.

Add $- 6$ and $0$ .

$y = - 6 + 0 + 0$

Add $- 6$ and $0$ .

$y = - 6 + 0$

Add $- 6$ and $0$ .

$y = - 6$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(- 9.38765153, 0)$

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