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

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

Find the x-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

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

$x \approx 0.28839189$

x-intercept(s) in point form.

x-intercept(s): $(0.28839189, 0)$

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

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

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

Multiply $- 6$ by $0$ .

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

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

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

Multiply $8$ by $0$ .

$y = 0 - 2 + 0 + 8 (0)$

Multiply $8$ by $0$ .

$y = 0 - 2 + 0 + 0$

Simplify by adding and subtracting.

Subtract $2$ from $0$ .

$y = - 2 + 0 + 0$

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): $(0.28839189, 0)$

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