Find the x and y Intercepts f(x)=8x^2-3-7x^3-2x

$f (x) = 8 x^{2} - 3 - 7 x^{3} - 2 x$

Step 1

Find the x-intercepts.

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

$0 = 8 x^{2} - 3 - 7 x^{3} - 2 x$

Solve the equation.

Remove parentheses.

$0 = 8 x^{2} - 3 - 7 x^{3} - 2 x$

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

$x \approx - 0.43808086$

x-intercept(s) in point form.

x-intercept(s): $(- 0.43808086, 0)$

Step 2

Find the y-intercepts.

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

$y = 8 {(0)}^{2} - 3 - 7 {(0)}^{3} - 2 \cdot 0$

Solve the equation.

Remove parentheses.

$y = 8 \cdot 0^{2} - 3 - 7 {(0)}^{3} - 2 \cdot 0$

Remove parentheses.

$y = 8 \cdot 0^{2} - 3 - 7 \cdot 0^{3} - 2 \cdot 0$

Remove parentheses.

$y = 8 {(0)}^{2} - 3 - 7 {(0)}^{3} - 2 \cdot 0$

Simplify $8 {(0)}^{2} - 3 - 7 {(0)}^{3} - 2 \cdot 0$ .

Simplify each term.

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

$y = 8 \cdot 0 - 3 - 7 {(0)}^{3} - 2 \cdot 0$

Multiply $8$ by $0$ .

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

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

$y = 0 - 3 - 7 \cdot 0 - 2 \cdot 0$

Multiply $- 7$ by $0$ .

$y = 0 - 3 + 0 - 2 \cdot 0$

Multiply $- 2$ by $0$ .

$y = 0 - 3 + 0 + 0$

Simplify by adding and subtracting.

Subtract $3$ from $0$ .

$y = - 3 + 0 + 0$

Add $- 3$ and $0$ .

$y = - 3 + 0$

Add $- 3$ and $0$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 3

List the intersections.

x-intercept(s): $(- 0.43808086, 0)$

y-intercept(s): $(0, - 3)$

Step 4

Find the x and y Intercepts f(x)=8x^2-3-7x^3-2x

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