Precalculus Examples

Rewrite the equation in vertex form.
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Complete the square for .
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Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
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Multiply by .
Move the negative in front of the fraction.
Find the value of using the formula .
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Simplify each term.
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Raise to the power of .
Multiply by .
Move the negative in front of the fraction.
Multiply .
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Multiply by .
Multiply by .
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 .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Add and .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Use the vertex form, , to determine the values of , , and .
Find the vertex .
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