# Precalculus Examples

Find the x and y Intercepts
To find the x-intercept, substitute in for and solve for .
Solve the equation.
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 .
Factor out of .
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 .
Factor out of .
Multiply by .
Multiply by .
Change the to .
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 .
Factor out of .
Multiply by .
Multiply by .
Change the to .
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 .
Raising to any positive power yields .
Subtract from .
These are the and intercepts of the equation .
x-intercept:
y-intercept: