Trigonometry Examples

Find the Vertex y^2-4x-8y-12=0
Rewrite the equation in vertex form.
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Isolate to the left side of the equation.
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Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Add to both sides of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify each term.
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Dividing two negative values results in a positive value.
Cancel the common factor of and .
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Factor out of .
Move the negative one from the denominator of .
Rewrite as .
Multiply by .
Divide by .
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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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Multiply by .
Find the value of using the formula .
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Simplify each term.
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Raise to the power of .
Combine and .
Divide by .
Divide by .
Multiply by .
Subtract from .
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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