# Precalculus Examples

To find the x-intercept, substitute in for and solve for .

Rewrite the equation as .

Add to both sides of the equation.

Move to the left side of the equation by subtracting it from both sides.

Factor the left side of the equation.

Rewrite as .

Since both terms are perfect cubes, factor using the difference of cubes formula, where and .

Simplify.

Multiply by .

One to any power is one.

Set equal to and solve for .

Set the factor equal to .

Add to both sides of the equation.

Set equal to and solve for .

Set the factor equal to .

Use the quadratic formula to find the solutions.

Substitute the values , , and into the quadratic formula and solve for .

Simplify.

Simplify the numerator.

One to any power is one.

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Multiply by .

Simplify the expression to solve for the portion of the .

Simplify the numerator.

One to any power is one.

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Multiply by .

Start simplifying.

Rewrite as .

Factor out of .

Factor out of .

Move the negative in front of the fraction.

Simplify the expression to solve for the portion of the .

Simplify the numerator.

One to any power is one.

Multiply by .

Multiply by .

Subtract from .

Rewrite as .

Rewrite as .

Rewrite as .

Multiply by .

Multiply by .

Start simplifying.

Rewrite as .

Factor out of .

Factor out of .

Move the negative in front of the fraction.

The final answer is the combination of both solutions.

The solution is the result of and .

To find the y-intercept, substitute in for and solve for .

Simplify each term.

Remove parentheses around .

Raising to any positive power yields .

Subtract from .

These are the and intercepts of the equation .

x-intercept:

y-intercept: