# Precalculus Examples

Complete the square for .
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 .
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.
Complete the square for .
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 .
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 .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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 .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
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 .

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