Find the x and y Intercepts x^3-6x-3

$x^{3} - 6 x - 3$

Step 1

Write $x^{3} - 6 x - 3$ as an equation.

$y = x^{3} - 6 x - 3$

Step 2

Find the x-intercepts.

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

$0 = x^{3} - 6 x - 3$

Solve the equation.

Remove parentheses.

$0 = x^{3} - 6 x - 3$

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

$x \approx - 2.14510269, - 0.52397639, 2.66907908$

x-intercept(s) in point form.

x-intercept(s): $(- 2.14510269, 0), (- 0.52397639, 0), (2.66907908, 0)$

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

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

$y = 0 - 6 \cdot 0 - 3$

Multiply $- 6$ by $0$ .

$y = 0 + 0 - 3$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$y = 0 - 3$

Subtract $3$ from $0$ .

$y = - 3$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(- 2.14510269, 0), (- 0.52397639, 0), (2.66907908, 0)$

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

Step 5