# Precalculus Examples

Reorder and .

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

Consider the vertex form of a parabola.

Find the value of using the formula .

Multiply by to get .

Multiply by to get .

Move the negative in front of the fraction.

Find the value of using the formula .

Simplify each term.

Multiply by to get .

Simplify the numerator.

Remove parentheses around .

Raise to the power of to get .

Simplify the denominator.

Remove parentheses.

Multiply by to get .

Multiply by to get .

Move the negative in front of the fraction.

Simplify .

Multiply by to get .

Multiply by to get .

Add and to get .

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

Substitute for in the equation .

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

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

Consider the vertex form of a parabola.

Find the value of using the formula .

Multiply by to get .

Multiply by to get .

Divide by to get .

Find the value of using the formula .

Simplify each term.

Multiply by to get .

Simplify the numerator.

Remove parentheses around .

Raise to the power of to get .

Simplify the denominator.

Remove parentheses.

Multiply by to get .

Multiply by to get .

Divide by to get .

Multiply by to get .

Add and to get .

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

Substitute for in the equation .

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

To write as a fraction with a common denominator, multiply by .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Multiply by to get .

Multiply by to get .

Subtract from to get .

To write as a fraction with a common denominator, multiply by .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Multiply by to get .

Subtract from to get .

Divide by to get .

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

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

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 .