Finite Math Examples

Find the Equation of the Parabola (-3,-9) , (6,-6) , (-3,2)
, ,
Step 1
Use the standard form of a quadratic equation as the starting point for finding the equation through the three points.
Step 2
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.
Step 3
Solve the system of equations to find the values of , , and .
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Step 3.1
Solve for in .
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Step 3.1.1
Rewrite the equation as .
Step 3.1.2
Simplify each term.
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Step 3.1.2.1
Raise to the power of .
Step 3.1.2.2
Move to the left of .
Step 3.1.2.3
Move to the left of .
Step 3.1.3
Move all terms not containing to the right side of the equation.
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Step 3.1.3.1
Subtract from both sides of the equation.
Step 3.1.3.2
Add to both sides of the equation.
Step 3.2
Replace all occurrences of with in each equation.
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Step 3.2.1
Replace all occurrences of in with .
Step 3.2.2
Simplify .
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Step 3.2.2.1
Simplify the left side.
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Step 3.2.2.1.1
Remove parentheses.
Step 3.2.2.2
Simplify the right side.
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Step 3.2.2.2.1
Simplify .
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Step 3.2.2.2.1.1
Simplify each term.
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Step 3.2.2.2.1.1.1
Raise to the power of .
Step 3.2.2.2.1.1.2
Move to the left of .
Step 3.2.2.2.1.1.3
Move to the left of .
Step 3.2.2.2.1.2
Simplify by adding terms.
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Step 3.2.2.2.1.2.1
Subtract from .
Step 3.2.2.2.1.2.2
Add and .
Step 3.2.3
Replace all occurrences of in with .
Step 3.2.4
Simplify .
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Step 3.2.4.1
Simplify the left side.
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Step 3.2.4.1.1
Remove parentheses.
Step 3.2.4.2
Simplify the right side.
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Step 3.2.4.2.1
Simplify .
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Step 3.2.4.2.1.1
Combine the opposite terms in .
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Step 3.2.4.2.1.1.1
Reorder the factors in the terms and .
Step 3.2.4.2.1.1.2
Add and .
Step 3.2.4.2.1.1.3
Add and .
Step 3.2.4.2.1.2
Simplify each term.
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Step 3.2.4.2.1.2.1
Raise to the power of .
Step 3.2.4.2.1.2.2
Move to the left of .
Step 3.2.4.2.1.3
Combine the opposite terms in .
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Step 3.2.4.2.1.3.1
Subtract from .
Step 3.2.4.2.1.3.2
Subtract from .
Step 3.3
Since is not true, there is no solution.
No solution
No solution