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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Solve for in the first equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the second equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Solve for in the third equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Simplify.
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Simplify the right side.
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Simplify each term.
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Multiply the numerator by the reciprocal of the denominator.
Simplify .
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Multiply and to get .
Multiply by to get .
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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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by to get .
Multiply by to get .
Subtract from to get .
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 .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Simplify the right side.
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Simplify each term.
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Simplify the numerator.
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Write as a fraction with denominator .
Multiply and to get .
Multiply the numerator by the reciprocal of the denominator.
Multiply by to get .
Simplify .
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Multiply and to get .
Multiply by to get .
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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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by to get .
Multiply by to get .
Add and to get .
Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
List the solutions to the system of equations.
Substitute the actual values of ,, and into the formula for a quadratic equation to find the resulting equation.
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