Find the x and y Intercepts f(x)=2-7x^3-7x^2-x

$f (x) = 2 - 7 x^{3} - 7 x^{2} - x$

Find the x-intercepts.

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

$0 = 2 - 7 x^{3} - 7 x^{2} - x$

Solve the equation.

Remove parentheses.

$0 = 2 - 7 x^{3} - 7 x^{2} - x$

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

$x \approx 0.40319702$

x-intercept(s) in point form.

x-intercept(s): $(0.40319702, 0)$

Find the y-intercepts.

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

$y = 2 - 7 {(0)}^{3} - 7 {(0)}^{2} - (0)$

Solve the equation.

Remove parentheses.

$y = 2 - 7 \cdot 0^{3} - 7 {(0)}^{2} - (0)$

Remove parentheses.

$y = 2 - 7 \cdot 0^{3} - 7 \cdot 0^{2} - (0)$

Remove parentheses.

$y = 2 - 7 {(0)}^{3} - 7 {(0)}^{2} - (0)$

Simplify $2 - 7 {(0)}^{3} - 7 {(0)}^{2} - (0)$ .

Simplify each term.

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

$y = 2 - 7 \cdot 0 - 7 {(0)}^{2} - (0)$

Multiply $- 7$ by $0$ .

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

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

$y = 2 + 0 - 7 \cdot 0 - (0)$

Multiply $- 7$ by $0$ .

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

Simplify by adding numbers.

Add $2$ and $0$ .

$y = 2 + 0 - (0)$

Add $2$ and $0$ .

$y = 2 - (0)$

Subtract $0$ from $2$ .

$y = 2$

y-intercept(s) in point form.

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

List the intersections.

x-intercept(s): $(0.40319702, 0)$

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