# Algebra Examples

Find the Standard Form of the Parabola
Step 1
Write as an equation.
Step 2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 3
Subtract from both sides of the equation.
Step 4
Complete the square.
Step 4.1
Reorder and .
Step 4.2
Use the form , to find the values of , , and .
Step 4.3
Consider the vertex form of a parabola.
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
Multiply by .
Step 4.4.2.2
Move the negative in front of the fraction.
Step 4.5
Find the value of using the formula .
Step 4.5.1
Substitute the values of , and into the formula .
Step 4.5.2
Simplify the right side.
Step 4.5.2.1
Simplify each term.
Step 4.5.2.1.1
Raise to the power of .
Step 4.5.2.1.2
Multiply by .
Step 4.5.2.2
Subtract from .
Step 4.6
Substitute the values of , , and into the vertex form .
Step 5
Move all terms not containing to the right side of the equation.
Step 5.1
Add to both sides of the equation.
Step 5.2
To write as a fraction with a common denominator, multiply by .
Step 5.3
Combine and .
Step 5.4
Combine the numerators over the common denominator.
Step 5.5
Simplify the numerator.
Step 5.5.1
Multiply by .
Step 5.5.2
Step 5.6
Move the negative in front of the fraction.
Step 6
Divide each term in by and simplify.
Step 6.1
Divide each term in by .
Step 6.2
Simplify the left side.
Step 6.2.1
Cancel the common factor of .
Step 6.2.1.1
Cancel the common factor.
Step 6.2.1.2
Divide by .
Step 6.3
Simplify the right side.
Step 6.3.1
Simplify each term.
Step 6.3.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 6.3.1.2
Multiply .
Step 6.3.1.2.1
Multiply by .
Step 6.3.1.2.2
Multiply by .
Step 7
Factor.
Step 7.1
To write as a fraction with a common denominator, multiply by .
Step 7.2
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Step 7.2.1
Multiply by .
Step 7.2.2
Multiply by .
Step 7.3
Combine the numerators over the common denominator.
Step 7.4
Move to the left of .
Step 7.5
Reorder terms.