1. Warm-Up 1 (9.29.2014) 1) x2 – 7x + 12 = 0 (by factoring)
Find the zeros of the following:
1) x2 – 7x + 12 = 0 (by factoring)
2) x2 + 4x – 16 = 0 (by quadratic Formula)
3) 2x2 + 8 = 0 (by sqrt method)

2. Essential Question ( )
How does the discriminant describe a quadratic function based on its solutions?

3. Ways to Solve Quadratic Equations and When to use each:
Factor – Use if you can easily determine the factors
Graphing – If you have access to a graphing calculator (Never preferred method anymore!)
Solving for x – Use if there is no “b” value
Quadratic Formula – ALWAYS works!

4. Types of Graphs:
Graph the following Quadratics, complete a very rough sketch of the graph. (Just show the approximate x-intercepts from your calculator)

5. How many times does each quadratic touch the x-axis?

6. How many solutions does each quadratic have?
The number of times a quadratic touches the x-axis is the number of solutions for the quadratic!!! 1. 2. 3.

7. Recall from the previous lesson, the quadratic formula: The Discriminant of the quadratic formula helps us to determine how many solutions a quadratic will have: The Discriminant is

8. What is the discriminate for each quadratic?

9. Discriminant:
If is a positive number there will be 2 real solutions If is zero there will be 1 solution. If is a negative number there will be 0 real solutions (2 nonreal #s)

10. EVERYTHING I NEED TO KNOW ABOUT the Discriminant!
Value of the discriminant
(b2 – 4ac)
Number and type of roots
What does the graph look like?
b2 – 4ac is positive
b2 – 4ac > 0
b2 – 4ac = 0
b2 – 4ac is negative
b2 – 4ac < 0
Crosses x-axis twice
2 real roots
Crosses x-axis once (x-intercept is the same as the vertex!)
1 real root
No real roots
(2 Imaginary)
Never crosses the x-axis!

11. Given the following quadratics, use the discriminant to determine how many solutions it will have.
1. x2 – 6x + 11 = x2 + 5x = 12
3. 3x = x2 – 27 = 0
5. x2 + x + 1 = x2 + 4x -1 = 0

12. Given the following graphs of a quadratic function:
Determine the sign of the discriminant.
Determine whether the solutions are real or imaginary.

13. Summary: What two methods of solving quadratics will ALWAYS give you an answer? How do you know when to use square roots to solve? What are 2 other terms for the x – intercepts of a quadratic function?