# Precalculus Examples

Step 1
Subtract from both sides of the equation.
Step 2
Complete the square for .
Step 2.1
Use the form , to find the values of , , and .
Step 2.2
Consider the vertex form of a parabola.
Step 2.3
Find the value of using the formula .
Step 2.3.1
Substitute the values of and into the formula .
Step 2.3.2
Cancel the common factor of and .
Step 2.3.2.1
Factor out of .
Step 2.3.2.2
Cancel the common factors.
Step 2.3.2.2.1
Factor out of .
Step 2.3.2.2.2
Cancel the common factor.
Step 2.3.2.2.3
Rewrite the expression.
Step 2.3.2.2.4
Divide by .
Step 2.4
Find the value of using the formula .
Step 2.4.1
Substitute the values of , and into the formula .
Step 2.4.2
Simplify the right side.
Step 2.4.2.1
Simplify each term.
Step 2.4.2.1.1
Cancel the common factor of and .
Step 2.4.2.1.1.1
Factor out of .
Step 2.4.2.1.1.2
Cancel the common factors.
Step 2.4.2.1.1.2.1
Factor out of .
Step 2.4.2.1.1.2.2
Cancel the common factor.
Step 2.4.2.1.1.2.3
Rewrite the expression.
Step 2.4.2.1.1.2.4
Divide by .
Step 2.4.2.1.2
Multiply by .
Step 2.4.2.2
Subtract from .
Step 2.5
Substitute the values of , , and into the vertex form .
Step 3
Substitute for in the equation .
Step 4
Move to the right side of the equation by adding to both sides.
Step 5
Complete the square for .
Step 5.1
Use the form , to find the values of , , and .
Step 5.2
Consider the vertex form of a parabola.
Step 5.3
Find the value of using the formula .
Step 5.3.1
Substitute the values of and into the formula .
Step 5.3.2
Cancel the common factor of and .
Step 5.3.2.1
Factor out of .
Step 5.3.2.2
Cancel the common factors.
Step 5.3.2.2.1
Factor out of .
Step 5.3.2.2.2
Cancel the common factor.
Step 5.3.2.2.3
Rewrite the expression.
Step 5.3.2.2.4
Divide by .
Step 5.4
Find the value of using the formula .
Step 5.4.1
Substitute the values of , and into the formula .
Step 5.4.2
Simplify the right side.
Step 5.4.2.1
Simplify each term.
Step 5.4.2.1.1
Raise to the power of .
Step 5.4.2.1.2
Multiply by .
Step 5.4.2.1.3
Divide by .
Step 5.4.2.1.4
Multiply by .
Step 5.4.2.2
Subtract from .
Step 5.5
Substitute the values of , , and into the vertex form .
Step 6
Substitute for in the equation .
Step 7
Move to the right side of the equation by adding to both sides.
Step 8
Simplify .
Step 8.1