Find the x and y Intercepts f(x)=-8x-1+8x^2+8x^3

$f (x) = - 8 x - 1 + 8 x^{2} + 8 x^{3}$

Step 1

Find the x-intercepts.

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

$0 = - 8 x - 1 + 8 x^{2} + 8 x^{3}$

Solve the equation.

Remove parentheses.

$0 = - 8 x - 1 + 8 x^{2} + 8 x^{3}$

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

$x \approx - 1.58212396, - 0.11356722, 0.69569119$

x-intercept(s) in point form.

x-intercept(s): $(- 1.58212396, 0), (- 0.11356722, 0), (0.69569119, 0)$

Step 2

Find the y-intercepts.

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

$y = - 8 \cdot 0 - 1 + 8 {(0)}^{2} + 8 {(0)}^{3}$

Solve the equation.

Remove parentheses.

$y = - 8 \cdot 0 - 1 + 8 \cdot 0^{2} + 8 {(0)}^{3}$

Remove parentheses.

$y = - 8 \cdot 0 - 1 + 8 \cdot 0^{2} + 8 \cdot 0^{3}$

Remove parentheses.

$y = - 8 \cdot 0 - 1 + 8 {(0)}^{2} + 8 {(0)}^{3}$

Simplify $- 8 \cdot 0 - 1 + 8 {(0)}^{2} + 8 {(0)}^{3}$ .

Simplify each term.

Multiply $- 8$ by $0$ .

$y = 0 - 1 + 8 {(0)}^{2} + 8 {(0)}^{3}$

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

$y = 0 - 1 + 8 \cdot 0 + 8 {(0)}^{3}$

Multiply $8$ by $0$ .

$y = 0 - 1 + 0 + 8 {(0)}^{3}$

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

$y = 0 - 1 + 0 + 8 \cdot 0$

Multiply $8$ by $0$ .

$y = 0 - 1 + 0 + 0$

Simplify by adding and subtracting.

Subtract $1$ from $0$ .

$y = - 1 + 0 + 0$

Add $- 1$ and $0$ .

$y = - 1 + 0$

Add $- 1$ and $0$ .

$y = - 1$

y-intercept(s) in point form.

y-intercept(s): $(0, - 1)$

Step 3

List the intersections.

x-intercept(s): $(- 1.58212396, 0), (- 0.11356722, 0), (0.69569119, 0)$

y-intercept(s): $(0, - 1)$

Step 4

Find the x and y Intercepts f(x)=-8x-1+8x^2+8x^3

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