Find the Focus 12(y+3)=(x-4)^2

Math
Rewrite the equation in vertex form.
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Isolate to the left side of the equation.
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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 .
Subtract from both sides of the equation.
Reorder terms.
Complete the square for .
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Simplify each term.
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Rewrite as .
Expand using the FOIL Method.
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Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
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Simplify each term.
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Multiply by .
Move to the left of .
Multiply by .
Subtract from .
Apply the distributive property.
Simplify.
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Combine and .
Cancel the common factor of .
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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Combine and .
Cancel the common factor of .
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Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Move the negative in front of the fraction.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Move the negative in front of the fraction.
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 the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Multiply and .
Combine and .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out 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 .
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Simplify each term.
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Simplify the numerator.
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Apply the product rule to .
Raise to the power of .
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Combine and .
Multiply by .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Subtract from .
Divide by .
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 .
Find , the distance from the vertex to the focus.
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Find the distance from the vertex to a focus of the parabola by using the following formula.
Substitute the value of into the formula.
Simplify.
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Combine and .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Find the focus.
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The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Substitute the known values of , , and into the formula and simplify.
Find the Focus 12(y+3)=(x-4)^2

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