Precalculus Examples

Set the polynomial equal to to find the properties of the parabola.
Complete the square on the right side of the equation.
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Find the value of using the formula .
Multiply by to get .
Multiply by to get .
Find the value of using the formula .
Simplify each term.
Multiply by to get .
Simplify the numerator.
Remove parentheses around .
Raise to the power of to get .
Simplify the denominator.
Remove parentheses.
Multiply by to get .
Multiply by to get .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Move the negative in front of the fraction.
Substitute the values of , , and into the vertex form .
Reorder the right side of the equation to match the vertex form of a parabola.
Use the vertex form, , to determine the values of , , and .
Find the vertex .

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