Precalculus Examples

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 .
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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Multiply by .
Simplify the numerator.
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Remove parentheses around .
Raise to the power of .
Simplify the denominator.
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Remove parentheses.
Multiply by .
Multiply by .
Move the negative in front of the fraction.
Simplify .
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Multiply by .
Multiply by .
Add and .
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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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 .
Multiply by .
Divide by .
Find the value of using the formula .
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Simplify each term.
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Multiply by .
Simplify the numerator.
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Remove parentheses around .
Raise to the power of .
Simplify the denominator.
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Remove parentheses.
Multiply by .
Multiply by .
Divide by .
Multiply by .
Add and .
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.
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 .
Multiply by .
Subtract from .
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 .
Subtract from .
Divide by .
Flip the sign on each term of the equation so the term on the right side is positive.
Divide each term by to make the right side equal to one.
Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .
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