Find the Equation of the Parabola (1,-12) , (2,-7) , (5,80)

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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One to any power is one.
Multiply by .
Multiply by .
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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Simplify .
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Simplify each term.
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Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Multiply by .
Simplify by adding terms.
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Add and .
Add and .
Simplify .
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Simplify each term.
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Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Multiply by .
Simplify by adding terms.
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Add and .
Add and .
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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Add to both sides of the equation.
Add to both sides of the equation.
Add and .
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 each term.
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Move the negative in front of the fraction.
Move the negative in front of the fraction.
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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Simplify .
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Simplify each term.
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Apply the distributive property.
Multiply .
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Multiply by .
Multiply by .
Multiply .
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Multiply by .
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 .
To write as a fraction with a common denominator, multiply by .
Simplify terms.
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Combine and .
Combine the numerators over the common denominator.
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Simplify .
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Simplify each term.
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Apply the distributive property.
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.
Multiply by .
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.
Multiply by .
Simplify by adding terms.
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Add and .
Subtract from .
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.
Tap for more steps…
Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
Tap for more steps…
Divide each term in by .
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Divide by .
Divide by .
Replace all occurrences of with in each equation.
Tap for more steps…
Replace all occurrences of in with .
Replace all occurrences of in with .
Simplify.
Tap for more steps…
Remove parentheses.
Simplify .
Tap for more steps…
Subtract from .
Divide by .
Simplify .
Tap for more steps…
Simplify each term.
Tap for more steps…
Multiply by .
Move the negative in front of the fraction.
Multiply .
Tap for more steps…
Multiply by .
Multiply by .
Combine the numerators over the common denominator.
Add and .
Divide by .
Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.
Find the Equation of the Parabola (1,-12) , (2,-7) , (5,80)


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