Graph (y plus one) to the power of two equals twelve(x plus one)

Graph (y+1)^2=12(x+1)
Should be rewritten the equation as .
First, divide each term by and simplify.
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Divide each term in by .
The common factor should be canceled of .
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Cancel the common factor.
Divide by .
Subtract from both sides of the equation.
Calculate the properties of the given parabola.
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Reformulate the equation as the vertex.
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Shift terms.
Complete the square for .
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Clarify each term.
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Rewrite as .
Expand using the FOIL Method.
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Use the distributive law.
Apply the distributive property.
Apply the distributive property.
Clarify and Add like terms.
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Clarify each term.
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First, multiply by .
Multiply by .
Multiply by .
First, multiply by .
Add and .
Apply the distributive property.
Simplify.
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Combine and .
The common factor should be canceled.
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Factor out of .
Factor out of .
Cancel the common factor.
Reformulate the expression.
Combine and .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Add numerators over the common denominator.
Clarify the numerator.
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Multiply by .
Subtract from .
Put the negative in front of the fraction.
Consider the form, to find the values of , , and .
Consider the vertex form of a parabola.
Replace the values of and into the formula .
Clarify the right side.
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Multiply the numerator by the denominator's reciprocal.
Combine and .
Cancel the common factor of and .
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Factor out of .
The common factors should be canceled.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
The common factor should be canceled.
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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 raised to any power equals one.
Raise to the power of .
Combine and .
The common factor should be canceled 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.
The common factor should be canceled.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Add fractions.
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Combine the numerators over the common denominator.
Clarify 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.
Consider the vertex form, , to determine the values of , , and .
Since the value of is positive, the parabola opens right.
Opens Right
Find the vertex .
Calculate , 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 .
Calculate 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.
Replace the known values of , , and into the formula and simplify.
Calculate the axis of symmetry by Calculateing the line that passes through the vertex and the focus.
Calculate 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.
Analyze and plot the parabola using its characteristics.
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 such a case, the point is .
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Replace the variable with in the expression.
Clarify the result.
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Simplify each term.
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Sum and .
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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Sum and .
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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Add and .
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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Add and .
Multiply by .
The final answer is .
Convert to decimal.
Use the characteristics and points to plot the parabola.
Graph the parabola using its properties and the selected points.
Direction: Opens Right
Vertex:
Focus:
Axis of Symmetry:
Directrix:
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