Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Find the value of using the formula .
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Simplify each term.
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Raising to any positive power yields .
Combine and .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Multiply by .
Add and .
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 .
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 verticalline 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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Multiply by .
Add and .
The final answer is .
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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Multiply by .
Add and .
The final answer is .
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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Multiply by .
Add and .
The final answer is .
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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Multiply by .
Add and .
The final answer is .
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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