1. What you will learn
How to solve a quadratic equation using the quadratic formula
How to classify the solutions of a quadratic equation based on the discriminant

2. Oh Boy! Vocabulary
We have learned about a million ways to solve quadratic equations:
factoring
taking square roots
completing the square
Clearly, we need another way: the quadratic formula:
Objective: 5.6 The Quadratic Formula and the Discriminant

3. A, B, and C?
When the quadratic equation is in the form ax2 + bx + c = 0
This will give you the values of x that cause the equation to be equal to zero.
This also gives you the two points where the graph of the function will cross the x-axis.
Objective: 5.6 The Quadratic Formula and the Discriminant

4. What Are Solutions 1 real solution 2 real solutions
In addition to being the values of x that satisfy the equation (in this case when the function equals zero), the “answers” are the places where the graph of the function crosses the x-axis. A graph can tell you how many solutions a quadratic function has.
1 real solution
2 real solutions
No real solutions (imaginary)
Objective: 5.6 The Quadratic Formula and the Discriminant

5. An Example – Two Solutions
Solve 2x2 + x = 5
Check this with your calculator.
Objective: 5.6 The Quadratic Formula and the Discriminant

6. You Try!
Solve: 3x2 + 8x = 35
Objective: 5.6 The Quadratic Formula and the Discriminant

7. An Example – One Solution
Solve x2 – x = 5x – 9
This equation will only touch the x-axis in one spot.
Objective: 5.6 The Quadratic Formula and the Discriminant

8. You Try
Solve 12x – 5 = 2x2 + 13
Objective: 5.6 The Quadratic Formula and the Discriminant

9. An Example – Two Imaginary Solutions
Solve –x2 + 2x = 2
If the solution has an “i” in it, the graph never crosses the x-axis.
Objective: 5.6 The Quadratic Formula and the Discriminant

10. You Try
Solve -2x2 = -2x + 3
Objective: 5.6 The Quadratic Formula and the Discriminant

11. The Discrimiwhat? Discriminant
The discriminant can also tell us what types of solutions there are to a quadratic equation.
If the discriminant is > 0, the equation has two real solutions
If the discriminant = 0, then the equation has one real solution.
If the discriminant is < 0, then the equation has two imaginary solutions.
Objective: 5.6 The Quadratic Formula and the Discriminant

12. Example Find the discriminant of the following: x2 – 6x + 10 = 0
Calculator check!
Objective: 5.6 The Quadratic Formula and the Discriminant

13. Homework
Page 295, even, 28, even, even, all, 78.
Objective: 5.6 The Quadratic Formula and the Discriminant