# Graph (y+5/2)^2=-5(x-9/2)

Rewrite the equation as .

Divide each term in by and simplify.

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Divide each term in by .

Simplify the left side.

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Cancel the common factor of .

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Cancel the common factor.

Divide by .

Simplify the right side.

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Simplify the numerator.

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To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Move to the left of .

Apply the product rule to .

Raise to the power of .

Multiply the numerator by the reciprocal of the denominator.

Combine.

Simplify the expression.

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Multiply by .

Multiply by .

Move the negative in front of the fraction.

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 the expression.

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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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Rewrite using the commutative property of multiplication.

Multiply by by adding the exponents.

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Move .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Add and .

Apply the distributive property.

Simplify.

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Cancel the common factor of .

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Move the leading negative in into the numerator.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Cancel the common factor of .

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Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

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Move the leading negative in into the numerator.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Multiply by .

Simplify each term.

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Move the negative in front of the fraction.

Rewrite as .

Move the negative in front of the fraction.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

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Multiply and .

Multiply by .

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.

Find the value of using the formula .

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Substitute the values of and into the formula .

Simplify the right side.

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Dividing two negative values results in a positive value.

Combine and .

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Find the value of using the formula .

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Substitute the values of , and into the formula .

Simplify the right side.

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Simplify each term.

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Raise to the power of .

Simplify the denominator.

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Multiply by .

Combine and .

Move the negative in front of the fraction.

Cancel the common factor of and .

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Rewrite as .

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply .

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Multiply by .

Multiply by .

Combine the numerators over the common denominator.

Add 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.

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 negative, the parabola opens left.

Opens Left

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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Cancel the common factor of and .

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Rewrite as .

Move the negative in front of the fraction.

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 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 Left

Vertex:

Focus:

Axis of Symmetry:

Directrix:

Direction: Opens Left

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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Multiply by .

Subtract from .

Reduce the expression by cancelling the common factors.

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Reduce the expression by cancelling the common factors.

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Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Combine exponents.

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Multiply by .

Multiply by .

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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Simplify each term.

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Multiply by .

Subtract from .

Reduce the expression by cancelling the common factors.

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Reduce the expression by cancelling the common factors.

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Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Combine exponents.

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Multiply by .

Multiply by .

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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Simplify each term.

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Multiply by .

Subtract from .

Reduce the expression by cancelling the common factors.

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Reduce the expression by cancelling the common factors.

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Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Combine exponents.

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Multiply by .

Multiply by .

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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Simplify each term.

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Multiply by .

Subtract from .

Reduce the expression by cancelling the common factors.

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Reduce the expression by cancelling the common factors.

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Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Combine exponents.

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Multiply by .

Multiply by .

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 Left

Vertex:

Focus:

Axis of Symmetry:

Directrix:

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