Find the x and y Intercepts f(x)=-2-6x-8x^3+8x^2

$f (x) = - 2 - 6 x - 8 x^{3} + 8 x^{2}$

Find the x-intercepts.

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

$0 = - 2 - 6 x - 8 x^{3} + 8 x^{2}$

Solve the equation.

Remove parentheses.

$0 = - 2 - 6 x - 8 x^{3} + 8 x^{2}$

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

$x \approx - 0.23898362$

x-intercept(s) in point form.

x-intercept(s): $(- 0.23898362, 0)$

Find the y-intercepts.

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

$y = - 2 - 6 \cdot 0 - 8 {(0)}^{3} + 8 {(0)}^{2}$

Solve the equation.

Remove parentheses.

$y = - 2 - 6 \cdot 0 - 8 \cdot 0^{3} + 8 {(0)}^{2}$

Remove parentheses.

$y = - 2 - 6 \cdot 0 - 8 \cdot 0^{3} + 8 \cdot 0^{2}$

Remove parentheses.

$y = - 2 - 6 \cdot 0 - 8 {(0)}^{3} + 8 {(0)}^{2}$

Simplify $- 2 - 6 \cdot 0 - 8 {(0)}^{3} + 8 {(0)}^{2}$ .

Simplify each term.

Multiply $- 6$ by $0$ .

$y = - 2 + 0 - 8 {(0)}^{3} + 8 {(0)}^{2}$

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

$y = - 2 + 0 - 8 \cdot 0 + 8 {(0)}^{2}$

Multiply $- 8$ by $0$ .

$y = - 2 + 0 + 0 + 8 {(0)}^{2}$

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

$y = - 2 + 0 + 0 + 8 \cdot 0$

Multiply $8$ by $0$ .

$y = - 2 + 0 + 0 + 0$

Simplify by adding numbers.

Add $- 2$ and $0$ .

$y = - 2 + 0 + 0$

Add $- 2$ and $0$ .

$y = - 2 + 0$

Add $- 2$ and $0$ .

$y = - 2$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(- 0.23898362, 0)$

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