Precalculus Examples

Move all variables to the left side and all constants to the right side.
Complete the square for .
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Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Find the value of using the formula .
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Multiply by to get .
Multiply by to get .
Find the value of using the formula .
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Simplify each term.
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Multiply by to get .
Raise to the power of to get .
Multiply by to get .
Subtract from to get .
Substitute the values of , , and into the vertex form .
Substitute for in the equation .
Move to the right side of the equation by adding to both sides.
Complete the square for .
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Reorder and .
Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Find the value of using the formula .
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Multiply by to get .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Rewrite the expression.
Find the value of using the formula .
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Simplify each term.
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Multiply by to get .
Simplify the numerator.
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Remove parentheses around .
One to any power is one.
Simplify the denominator.
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Remove parentheses.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Substitute the values of , , and into the vertex form .
Substitute for in the equation .
Move to the right side of the equation by adding to both sides.
Find the common denominator.
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Write as a fraction with denominator .
Multiply by .
Multiply and to get .
Combine fractions.
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Combine the numerators over the common denominator.
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by to get .
Add and to get .
Add and to get .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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