# Precalculus Examples

Step 1

Step 1.1

Use the form , to find the values of , , and .

Step 1.2

Consider the vertex form of a parabola.

Step 1.3

Find the value of using the formula .

Step 1.3.1

Substitute the values of and into the formula .

Step 1.3.2

Cancel the common factor of and .

Step 1.3.2.1

Factor out of .

Step 1.3.2.2

Cancel the common factors.

Step 1.3.2.2.1

Factor out of .

Step 1.3.2.2.2

Cancel the common factor.

Step 1.3.2.2.3

Rewrite the expression.

Step 1.3.2.2.4

Divide by .

Step 1.4

Find the value of using the formula .

Step 1.4.1

Substitute the values of , and into the formula .

Step 1.4.2

Simplify the right side.

Step 1.4.2.1

Simplify each term.

Step 1.4.2.1.1

Cancel the common factor of and .

Step 1.4.2.1.1.1

Factor out of .

Step 1.4.2.1.1.2

Cancel the common factors.

Step 1.4.2.1.1.2.1

Factor out of .

Step 1.4.2.1.1.2.2

Cancel the common factor.

Step 1.4.2.1.1.2.3

Rewrite the expression.

Step 1.4.2.1.1.2.4

Divide by .

Step 1.4.2.1.2

Multiply by .

Step 1.4.2.2

Subtract from .

Step 1.5

Substitute the values of , , and into the vertex form .

Step 2

Substitute for in the equation .

Step 3

Move to the right side of the equation by adding to both sides.

Step 4

Step 4.1

Use the form , to find the values of , , and .

Step 4.2

Consider the vertex form of a parabola.

Step 4.3

Find the value of using the formula .

Step 4.3.1

Substitute the values of and into the formula .

Step 4.3.2

Simplify the right side.

Step 4.3.2.1

Cancel the common factor of and .

Step 4.3.2.1.1

Factor out of .

Step 4.3.2.1.2

Move the negative one from the denominator of .

Step 4.3.2.2

Rewrite as .

Step 4.3.2.3

Multiply by .

Step 4.4

Find the value of using the formula .

Step 4.4.1

Substitute the values of , and into the formula .

Step 4.4.2

Simplify the right side.

Step 4.4.2.1

Simplify each term.

Step 4.4.2.1.1

Raise to the power of .

Step 4.4.2.1.2

Multiply by .

Step 4.4.2.1.3

Divide by .

Step 4.4.2.1.4

Multiply by .

Step 4.4.2.2

Add and .

Step 4.5

Substitute the values of , , and into the vertex form .

Step 5

Substitute for in the equation .

Step 6

Move to the right side of the equation by adding to both sides.

Step 7

Step 7.1

Add and .

Step 7.2

Subtract from .

Step 8

Flip the sign on each term of the equation so the term on the right side is positive.

Step 9

Divide each term by to make the right side equal to one.

Step 10

Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .