6-5 The Quadratic Formula and the Discriminant Objectives Students will be able to: Solve quadratic equations by using the Quadratic Formula Use the discriminant to determine the number and type of roots of a quadratic equation

Using the quadratic formula is yet another way to solve quadratic equations. What is the quadratic formula? Perhaps it’s best explained through song… Quadratic Formula The formula Use the formula below to find the solutions of a quadratic equation in the form

So how do we use the quadratic formula So how do we use the quadratic formula? Solve the following equation using the quadratic formula:

Solve each equation by using the quadratic formula. 1)

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Try these. 5) 6)

The discriminant The discriminant is the expression within the quadratic formula that is The value of the discriminant can be used to determine the number and type of roots of a quadratic equation.

Find the value of the discriminant for each quadratic equation Find the value of the discriminant for each quadratic equation. Then describe the number and type of roots for the equation. 1) 2)

3) 4)

Try these. 5) 6)

There are times when you will be given a quadratic equation and be asked to solve. It is then up to you to determine which method you would like to use to solve. It is important to be able to distinguish between the different methods, and to know which methods will work all the time, and which methods will only work sometimes.