Trigonometry Examples

Find the Vertex y^2-4x-8y-12=0
Rewrite the equation in vertex form.
Isolate to the left side of the equation.
Move all terms not containing to the right side of the equation.
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.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify each term.
Dividing two negative values results in a positive value.
Cancel the common factor of and .
Factor out of .
Move the negative one from the denominator of .
Rewrite as .
Multiply by .
Divide by .
Complete the square for .
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.
Cancel the common factor of .
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 .
Simplify each term.
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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