1. 3.7: Solving Quadratic Equations by the Quadratic Formula

3. Objectives Learn the Quadratic Formula
Use the QF to determine the number of solutions to a quadratic function
Use the QF to find the solutions to a quadratic function

4. Concept: The Quadratic Formula
When a quadratic that is written in Standard Form , won’t factor apart nicely, we can still find the roots by using the:
Quadratic Formula:
The Quadratic Formula will let you
solve ANY quadratic equation.

5. Concept: The Discriminant:
The discriminant is the piece of the quadratic formula that is under the radical: b2 – 4ac

6. Concept: The Discriminant cont…
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.

7. Concept: The Discriminant cont…
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

8. Concept: The Discriminant cont…
Example #1
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)
a=2, b=7, c=-11
Discriminant =
Value of discriminant=137
Positive-NON perfect square
Nature of the Roots – 2 Reals - Irrational
Discriminant =

9. Concept: The Discriminant cont…
Example #1 continued
Solve using the Quadratic Formula

10. Concept: You Try!!!
Try the following examples. Do your work on your paper and then check your answers.