Graph (y+1)^2=12(x-4)

Graph (y+1)^2=12(x-4)
Rewrite the equation as .
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 .
Add to both sides of the equation.
Find the properties of the given parabola.
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Rewrite the equation in vertex form.
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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 .
Multiply by .
Multiply by .
Multiply by .
Add and .
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 .
Multiply by .
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 .
Add and .
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.
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.
Cancel the common factor of .
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Factor out of .
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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Simplify the numerator.
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Apply the product rule to .
One to any power is one.
Raise to the power of .
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.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine fractions.
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Combine the numerators over the common denominator.
Simplify the expression.
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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 .
Since the value of is positive, the parabola opens right.
Opens Right
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 x-coordinate if the parabola opens left or right.
Substitute the known values of , , and into the formula and simplify.
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
Find the directrix.
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The directrix of a parabola is the vertical line found by subtracting from the x-coordinate of the vertex if the parabola opens left or right.
Substitute the known values of and into the formula and simplify.
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.
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Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Subtract from .
Multiply by .
The final answer is .
Convert to decimal.
Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Subtract from .
Multiply by .
The final answer is .
Convert to decimal.
Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Subtract from .
Multiply by .
The final answer is .
Convert to decimal.
Substitute the value into . In this case, the point is .
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Subtract from .
Multiply by .
The final answer is .
Convert to decimal.
Graph the parabola using its properties and the selected points.
Graph the parabola using its properties and the selected points.
Direction: Opens Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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