# Precalculus Examples

Step 1

Step 1.1

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

Step 1.2

Solve the equation.

Step 1.2.1

Rewrite the equation as .

Step 1.2.2

Add to both sides of the equation.

Step 1.2.3

Subtract from both sides of the equation.

Step 1.2.4

Factor the left side of the equation.

Step 1.2.4.1

Rewrite as .

Step 1.2.4.2

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

Step 1.2.4.3

Simplify.

Step 1.2.4.3.1

Multiply by .

Step 1.2.4.3.2

One to any power is one.

Step 1.2.5

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

Step 1.2.6

Set equal to and solve for .

Step 1.2.6.1

Set equal to .

Step 1.2.6.2

Add to both sides of the equation.

Step 1.2.7

Set equal to and solve for .

Step 1.2.7.1

Set equal to .

Step 1.2.7.2

Solve for .

Step 1.2.7.2.1

Use the quadratic formula to find the solutions.

Step 1.2.7.2.2

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

Step 1.2.7.2.3

Simplify.

Step 1.2.7.2.3.1

Simplify the numerator.

Step 1.2.7.2.3.1.1

One to any power is one.

Step 1.2.7.2.3.1.2

Multiply .

Step 1.2.7.2.3.1.2.1

Multiply by .

Step 1.2.7.2.3.1.2.2

Multiply by .

Step 1.2.7.2.3.1.3

Subtract from .

Step 1.2.7.2.3.1.4

Rewrite as .

Step 1.2.7.2.3.1.5

Rewrite as .

Step 1.2.7.2.3.1.6

Rewrite as .

Step 1.2.7.2.3.2

Multiply by .

Step 1.2.7.2.4

Simplify the expression to solve for the portion of the .

Step 1.2.7.2.4.1

Simplify the numerator.

Step 1.2.7.2.4.1.1

One to any power is one.

Step 1.2.7.2.4.1.2

Multiply .

Step 1.2.7.2.4.1.2.1

Multiply by .

Step 1.2.7.2.4.1.2.2

Multiply by .

Step 1.2.7.2.4.1.3

Subtract from .

Step 1.2.7.2.4.1.4

Rewrite as .

Step 1.2.7.2.4.1.5

Rewrite as .

Step 1.2.7.2.4.1.6

Rewrite as .

Step 1.2.7.2.4.2

Multiply by .

Step 1.2.7.2.4.3

Change the to .

Step 1.2.7.2.4.4

Rewrite as .

Step 1.2.7.2.4.5

Factor out of .

Step 1.2.7.2.4.6

Factor out of .

Step 1.2.7.2.4.7

Move the negative in front of the fraction.

Step 1.2.7.2.5

Simplify the expression to solve for the portion of the .

Step 1.2.7.2.5.1

Simplify the numerator.

Step 1.2.7.2.5.1.1

One to any power is one.

Step 1.2.7.2.5.1.2

Multiply .

Step 1.2.7.2.5.1.2.1

Multiply by .

Step 1.2.7.2.5.1.2.2

Multiply by .

Step 1.2.7.2.5.1.3

Subtract from .

Step 1.2.7.2.5.1.4

Rewrite as .

Step 1.2.7.2.5.1.5

Rewrite as .

Step 1.2.7.2.5.1.6

Rewrite as .

Step 1.2.7.2.5.2

Multiply by .

Step 1.2.7.2.5.3

Change the to .

Step 1.2.7.2.5.4

Rewrite as .

Step 1.2.7.2.5.5

Factor out of .

Step 1.2.7.2.5.6

Factor out of .

Step 1.2.7.2.5.7

Move the negative in front of the fraction.

Step 1.2.7.2.6

The final answer is the combination of both solutions.

Step 1.2.8

The final solution is all the values that make true.

Step 1.3

x-intercept(s) in point form.

x-intercept(s):

x-intercept(s):

Step 2

Step 2.1

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

Step 2.2

Solve the equation.

Step 2.2.1

Remove parentheses.

Step 2.2.2

Remove parentheses.

Step 2.2.3

Simplify .

Step 2.2.3.1

Raising to any positive power yields .

Step 2.2.3.2

Subtract from .

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

y-intercept(s):

Step 3

List the intersections.

x-intercept(s):

y-intercept(s):

Step 4