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Algebra Examples
Step 1
Step 1.1
Combine and .
Step 1.2
Complete the square for .
Step 1.2.1
Use the form , to find the values of , , and .
Step 1.2.2
Consider the vertex form of a parabola.
Step 1.2.3
Find the value of using the formula .
Step 1.2.3.1
Substitute the values of and into the formula .
Step 1.2.3.2
Simplify the right side.
Step 1.2.3.2.1
Cancel the common factor of and .
Step 1.2.3.2.1.1
Factor out of .
Step 1.2.3.2.1.2
Cancel the common factors.
Step 1.2.3.2.1.2.1
Cancel the common factor.
Step 1.2.3.2.1.2.2
Rewrite the expression.
Step 1.2.3.2.2
Multiply the numerator by the reciprocal of the denominator.
Step 1.2.3.2.3
Multiply by .
Step 1.2.4
Find the value of using the formula .
Step 1.2.4.1
Substitute the values of , and into the formula .
Step 1.2.4.2
Simplify the right side.
Step 1.2.4.2.1
Simplify each term.
Step 1.2.4.2.1.1
Raising to any positive power yields .
Step 1.2.4.2.1.2
Combine and .
Step 1.2.4.2.1.3
Multiply by .
Step 1.2.4.2.1.4
Divide by .
Step 1.2.4.2.1.5
Divide by .
Step 1.2.4.2.1.6
Multiply by .
Step 1.2.4.2.2
Add and .
Step 1.2.5
Substitute the values of , , and into the vertex form .
Step 1.3
Set equal to the new right side.
Step 2
Use the vertex form, , to determine the values of , , and .
Step 3
Find the vertex .
Step 4