Precalculus Examples

, ,
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 .
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Simplify each term.
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Raising to any positive power yields .
Multiply by .
Multiply by .
Combine the opposite terms in .
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Add and .
Add and .
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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One to any power is one.
Multiply by .
Multiply by .
Rewrite the equation as .
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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Remove parentheses.
Remove parentheses.
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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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.
Subtract from .
Replace all occurrences of in with .
Simplify .
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Simplify each term.
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Apply the distributive property.
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 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 .
Divide by .
Replace all occurrences of in with .
Simplify .
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Multiply by .
Subtract from .
Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.
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