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**Solving Quadratic Equations by the Quadratic Formula**

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**THE QUADRATIC FORMULA This is the quadratic formula!**

Just identify a, b, and c then substitute into the formula.

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**WHY USE THE QUADRATIC FORMULA?**

The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it. An important piece of the quadratic formula is what’s under the radical: b2 – 4ac This piece is called the discriminant.

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**WHY IS THE DISCRIMINANT IMPORTANT?**

The discriminant tells you the number and types of answers (roots) you will get. The discriminant can be +, –, or 0 which actually tells you a lot! Since the discriminant is under a radical, think about what it means if you have a positive or negative number or 0 under the radical.

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**WHAT THE DISCRIMINANT TELLS YOU!**

Value of the Discriminant Nature of the Solutions Negative 2 imaginary solutions Zero 1 Real Solution Positive – perfect square 2 Reals- Rational Positive – non-perfect square 2 Reals- Irrational

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**Example #1 a=2, b=7, c=-11 Discriminant = Discriminant =**

Find the value of the discriminant and describe the nature of the roots (real,imaginary, rational, irrational) of each quadratic equation. Then solve the equation using the quadratic formula) 1. a=2, b=7, c=-11 Discriminant = Value of discriminant=137 Positive-NON perfect square Nature of the Roots – 2 Reals - Irrational Discriminant =

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Example #1- continued Solve using the Quadratic Formula

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**Solving Quadratic Equations by the Quadratic Formula**

Try the following examples. Do your work on your paper and then check your answers.

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