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What is a Quadratic Equation? |
A quadratic equation is a single-variable equation in which the highest power on the variable is 2. The standard form is:
where
,
, and
are real numbers and
.
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Solving Quadratic Equations |
There are three methods for solving a quadratic equations:
- Factoring
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Factoring is a process of changing the form of an equation from the standard form into the product of two factors:
Once the equation is in this form, each factor is set equal to 0 and solved for x. This uses the Zero-Product Property that says if the product of two factors equals zero, then at least one of the factors must equal zero.
OR
- Completing the Square
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Completing the square is a process of changing the form of an equation from the standard form so that both sides are perfect squares:
Once it’s in this form, the solutions can be found by taking the square root of both sides and solving for x.
- Quadratic Formula
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The quadratic formula is:
I prefer this form:
where
is the discriminant
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Solve a Quadratic Equation |
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