Find the x and y Intercepts f(x)=-7-3x+6x^3+x^2

$f (x) = - 7 - 3 x + 6 x^{3} + x^{2}$

Find the x-intercepts.

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

$0 = - 7 - 3 x + 6 x^{3} + x^{2}$

Solve the equation.

Remove parentheses.

$0 = - 7 - 3 x + 6 x^{3} + x^{2}$

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

$x \approx 1.15009737$

x-intercept(s) in point form.

x-intercept(s): $(1.15009737, 0)$

Find the y-intercepts.

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

$y = - 7 - 3 \cdot 0 + 6 {(0)}^{3} + {(0)}^{2}$

Solve the equation.

Remove parentheses.

$y = - 7 - 3 \cdot 0 + 6 \cdot 0^{3} + {(0)}^{2}$

Remove parentheses.

$y = - 7 - 3 \cdot 0 + 6 \cdot 0^{3} + 0^{2}$

Remove parentheses.

$y = - 7 - 3 \cdot 0 + 6 {(0)}^{3} + {(0)}^{2}$

Simplify $- 7 - 3 \cdot 0 + 6 {(0)}^{3} + {(0)}^{2}$ .

Simplify each term.

Multiply $- 3$ by $0$ .

$y = - 7 + 0 + 6 {(0)}^{3} + {(0)}^{2}$

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

$y = - 7 + 0 + 6 \cdot 0 + {(0)}^{2}$

Multiply $6$ by $0$ .

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

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

$y = - 7 + 0 + 0 + 0$

Simplify by adding numbers.

Add $- 7$ and $0$ .

$y = - 7 + 0 + 0$

Add $- 7$ and $0$ .

$y = - 7 + 0$

Add $- 7$ and $0$ .

$y = - 7$

y-intercept(s) in point form.

y-intercept(s): $(0, - 7)$

List the intersections.

x-intercept(s): $(1.15009737, 0)$

y-intercept(s): $(0, - 7)$