Precalculus Examples

Step 1
Rewrite the equation in vertex form.
Step 1.1
Complete the square for .
Step 1.1.1
Use the form , to find the values of , , and .
Step 1.1.2
Consider the vertex form of a parabola.
Step 1.1.3
Find the value of using the formula .
Step 1.1.3.1
Substitute the values of and into the formula .
Step 1.1.3.2
Multiply by .
Step 1.1.4
Find the value of using the formula .
Step 1.1.4.1
Substitute the values of , and into the formula .
Step 1.1.4.2
Simplify the right side.
Step 1.1.4.2.1
Simplify each term.
Step 1.1.4.2.1.1
Raise to the power of .
Step 1.1.4.2.1.2
Multiply by .
Step 1.1.4.2.2
To write as a fraction with a common denominator, multiply by .
Step 1.1.4.2.3
Combine and .
Step 1.1.4.2.4
Combine the numerators over the common denominator.
Step 1.1.4.2.5
Simplify the numerator.
Step 1.1.4.2.5.1
Multiply by .
Step 1.1.4.2.5.2
Subtract from .
Step 1.1.4.2.6
Move the negative in front of the fraction.
Step 1.1.5
Substitute the values of , , and into the vertex form .
Step 1.2
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