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

$3 x - x^{3}$

Step 1

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

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

Step 2

Find the x-intercepts.

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

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

Solve the equation.

Rewrite the equation as $3 x - x^{3} = 0$ .

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

Factor $x$ out of $3 x - x^{3}$ .

Factor $x$ out of $3 x$ .

$x \cdot 3 - x^{3} = 0$

Factor $x$ out of $- x^{3}$ .

$x \cdot 3 + x (- x^{2}) = 0$

Factor $x$ out of $x \cdot 3 + x (- x^{2})$ .

$x (3 - x^{2}) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$3 - x^{2} = 0$

Set $x$ equal to $0$ .

$x = 0$

Set $3 - x^{2}$ equal to $0$ and solve for $x$ .

Set $3 - x^{2}$ equal to $0$ .

$3 - x^{2} = 0$

Solve $3 - x^{2} = 0$ for $x$ .

Subtract $3$ from both sides of the equation.

$- x^{2} = - 3$

Divide each term in $- x^{2} = - 3$ by $- 1$ and simplify.

Divide each term in $- x^{2} = - 3$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 3}{- 1}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x^{2} = 3$

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{3}, - \sqrt{3}$

The final solution is all the values that make $x (3 - x^{2}) = 0$ true.

$x = 0, \sqrt{3}, - \sqrt{3}$

x-intercept(s) in point form.

x-intercept(s): $(0, 0), (\sqrt{3}, 0), (- \sqrt{3}, 0)$

Step 3

Find the y-intercepts.

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

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

Solve the equation.

Remove parentheses.

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

Remove parentheses.

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

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

Simplify each term.

Multiply $3$ by $0$ .

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

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

$y = 0 - 0$

Multiply $- 1$ by $0$ .

$y = 0 + 0$

Add $0$ and $0$ .

$y = 0$

y-intercept(s) in point form.

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

Step 4

List the intersections.

x-intercept(s): $(0, 0), (\sqrt{3}, 0), (- \sqrt{3}, 0)$

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

Step 5

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

Related Questions

Support LCMGCF.com by disabling your adblocker.