# Algebra Examples

Find the Parabola Through (-1,-5) with Vertex (2,3)
,
Step 1
The general equation of a parabola with vertex is . In this case we have as the vertex and is a point on the parabola. To find , substitute the two points in .
Step 2
Using to solve for , .
Step 2.1
Rewrite the equation as .
Step 2.2
Simplify each term.
Step 2.2.1
Multiply by .
Step 2.2.2
Subtract from .
Step 2.2.3
Raise to the power of .
Step 2.2.4
Move to the left of .
Step 2.3
Move all terms not containing to the right side of the equation.
Step 2.3.1
Subtract from both sides of the equation.
Step 2.3.2
Subtract from .
Step 2.4
Divide each term in by and simplify.
Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
Step 2.4.2.1
Cancel the common factor of .
Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 2.4.3
Simplify the right side.
Step 2.4.3.1
Move the negative in front of the fraction.
Step 3
Using , the general equation of the parabola with the vertex and is .
Step 4
Solve for .
Step 4.1
Remove parentheses.
Step 4.2
Multiply by .
Step 4.3
Remove parentheses.
Step 4.4
Simplify .
Step 4.4.1
Simplify each term.
Step 4.4.1.1
Multiply by .
Step 4.4.1.2
Rewrite as .
Step 4.4.1.3
Expand using the FOIL Method.
Step 4.4.1.3.1
Apply the distributive property.
Step 4.4.1.3.2
Apply the distributive property.
Step 4.4.1.3.3
Apply the distributive property.
Step 4.4.1.4
Simplify and combine like terms.
Step 4.4.1.4.1
Simplify each term.
Step 4.4.1.4.1.1
Multiply by .
Step 4.4.1.4.1.2
Move to the left of .
Step 4.4.1.4.1.3
Multiply by .
Step 4.4.1.4.2
Subtract from .
Step 4.4.1.5
Apply the distributive property.
Step 4.4.1.6
Simplify.
Step 4.4.1.6.1
Combine and .
Step 4.4.1.6.2
Multiply .
Step 4.4.1.6.2.1
Multiply by .
Step 4.4.1.6.2.2
Combine and .
Step 4.4.1.6.2.3
Multiply by .
Step 4.4.1.6.2.4
Combine and .
Step 4.4.1.6.3
Multiply .
Step 4.4.1.6.3.1
Multiply by .
Step 4.4.1.6.3.2
Combine and .
Step 4.4.1.6.3.3
Multiply by .
Step 4.4.1.7
Simplify each term.
Step 4.4.1.7.1
Move to the left of .
Step 4.4.1.7.2
Move the negative in front of the fraction.
Step 4.4.2
To write as a fraction with a common denominator, multiply by .
Step 4.4.3
Combine and .
Step 4.4.4
Combine the numerators over the common denominator.
Step 4.4.5
Simplify the numerator.
Step 4.4.5.1
Multiply by .
Step 4.4.5.2