Find the x and y Intercepts f(x)=7x^3+7x+4+9x^2

$f (x) = 7 x^{3} + 7 x + 4 + 9 x^{2}$

Find the x-intercepts.

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

$0 = 7 x^{3} + 7 x + 4 + 9 x^{2}$

Solve the equation.

Remove parentheses.

$0 = 7 x^{3} + 7 x + 4 + 9 x^{2}$

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

$x \approx - 0.88525878$

x-intercept(s) in point form.

x-intercept(s): $(- 0.88525878, 0)$

Find the y-intercepts.

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

$y = 7 {(0)}^{3} + 7 (0) + 4 + 9 {(0)}^{2}$

Solve the equation.

Remove parentheses.

$y = 7 \cdot 0^{3} + 7 (0) + 4 + 9 {(0)}^{2}$

Remove parentheses.

$y = 7 \cdot 0^{3} + 7 (0) + 4 + 9 \cdot 0^{2}$

Remove parentheses.

$y = 7 {(0)}^{3} + 7 (0) + 4 + 9 {(0)}^{2}$

Simplify $7 {(0)}^{3} + 7 (0) + 4 + 9 {(0)}^{2}$ .

Simplify each term.

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

$y = 7 \cdot 0 + 7 (0) + 4 + 9 {(0)}^{2}$

Multiply $7$ by $0$ .

$y = 0 + 7 (0) + 4 + 9 {(0)}^{2}$

Multiply $7$ by $0$ .

$y = 0 + 0 + 4 + 9 {(0)}^{2}$

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

$y = 0 + 0 + 4 + 9 \cdot 0$

Multiply $9$ by $0$ .

$y = 0 + 0 + 4 + 0$

Simplify by adding numbers.

Add $0$ and $0$ .

$y = 0 + 4 + 0$

Add $0$ and $4$ .

$y = 4 + 0$

Add $4$ and $0$ .

$y = 4$

y-intercept(s) in point form.

y-intercept(s): $(0, 4)$

List the intersections.

x-intercept(s): $(- 0.88525878, 0)$

y-intercept(s): $(0, 4)$