Find the Equation of the Parabola (3,1) , (-3,-5) , (9,-5)

Math
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Use the standard form of a quadratic equation as the starting point for finding the equation through the three points.
Create a system of equations by substituting the and values of each point into the standard formula of a quadratic equation to create the three equation system.
Solve the system of equations to find the values of , , and .
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Simplify each equation.
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Remove parentheses.
Simplify each term.
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Raise to the power of .
Move to the left of .
Move to the left of .
Remove parentheses.
Simplify each term.
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Raise to the power of .
Move to the left of .
Move to the left of .
Remove parentheses.
Simplify each term.
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Raise to the power of .
Move to the left of .
Move to the left of .
Solve for in the first equation.
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Rewrite the equation as .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from both sides of the equation.
Replace all occurrences of with in each equation.
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Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify each equation.
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Remove parentheses.
Simplify .
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Combine the opposite terms in .
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Subtract from .
Add and .
Subtract from .
Remove parentheses.
Simplify .
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Subtract from .
Subtract from .
Solve for in the second equation.
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Rewrite the equation as .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from .
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 .
Divide by .
Replace all occurrences of with in each equation.
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Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify.
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Simplify .
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Multiply by .
Subtract from .
Simplify .
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Multiply by .
Add and .
Solve for in the third equation.
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Rewrite the equation as .
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from .
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 .
Simplify .
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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.
Move the negative in front of the fraction.
Replace all occurrences of in with .
Simplify .
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Simplify each term.
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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 .
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 .
Subtract from .
Move the negative in front of the fraction.
Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.
Find the Equation of the Parabola (3,1) , (-3,-5) , (9,-5)

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