Find the x and y Intercepts f(x)=9x^3+5x-2x^2+2

$f (x) = 9 x^{3} + 5 x - 2 x^{2} + 2$

Find the x-intercepts.

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

$0 = 9 x^{3} + 5 x - 2 x^{2} + 2$

Solve the equation.

Remove parentheses.

$0 = 9 x^{3} + 5 x - 2 x^{2} + 2$

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

$x \approx - 0.30883038$

x-intercept(s) in point form.

x-intercept(s): $(- 0.30883038, 0)$

Find the y-intercepts.

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

$y = 9 {(0)}^{3} + 5 (0) - 2 {(0)}^{2} + 2$

Solve the equation.

Remove parentheses.

$y = 9 \cdot 0^{3} + 5 (0) - 2 {(0)}^{2} + 2$

Remove parentheses.

$y = 9 \cdot 0^{3} + 5 (0) - 2 \cdot 0^{2} + 2$

Remove parentheses.

$y = 9 {(0)}^{3} + 5 (0) - 2 {(0)}^{2} + 2$

Simplify $9 {(0)}^{3} + 5 (0) - 2 {(0)}^{2} + 2$ .

Simplify each term.

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

$y = 9 \cdot 0 + 5 (0) - 2 {(0)}^{2} + 2$

Multiply $9$ by $0$ .

$y = 0 + 5 (0) - 2 {(0)}^{2} + 2$

Multiply $5$ by $0$ .

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

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

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

Multiply $- 2$ by $0$ .

$y = 0 + 0 + 0 + 2$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 0 + 2$

Add $0$ and $0$ .

$y = 0 + 2$

Add $0$ and $2$ .

$y = 2$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(- 0.30883038, 0)$

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