# Precalculus Examples

Step 1
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 .
Substitute the values of and into the formula .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Find the value of using the formula .
Substitute the values of , and into the formula .
Simplify the right side.
Simplify each term.
Raise to the power of .
Multiply by .
Divide by .
Multiply by .
Subtract from .
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
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 .
Substitute the values of and into the formula .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Find the value of using the formula .
Substitute the values of , and into the formula .
Simplify the right side.
Simplify each term.
Raise to the power of .
Multiply by .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Subtract from .
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
Simplify .