1. Algebra
9.6
The Discriminant

2. √ The Discriminant + b² - 4ac - b - x = 2a
In the quadratic formula, the expression inside the radical is the discriminant. √ +
b² - 4ac
- b -
x = 2a
The discriminant can be used to find the number of solutions a quadratic equation has.

3. Before using Quadratic Formula to solve…….
Compute the value of b²- 4ac
If the value is:
There are 2 solutions
POSITIVE
There is 1 solution
ZERO
There are no real solutions
NEGATIVE

4. How b²- 4ac effects the Quadratic Formula
POSITIVE numbers have 2 square roots
NEGATIVE numbers don’t have square roots
ZERO has 1 square root
2 solutions
1 solution
no real solutions

5. Try it with these equations
Compute the value of b²- 4ac
x²- 3x – 4 = 0
(-3)²- 4(1)(-4) = = 25
positive, 2 solutions
-x²+ 2x – 1 = 0
(2)²- 4(-1)(-1) = = 0
zero, 1 solution
2x²- 2x + 3 = 0
(-2)²- 4(2)(3) = = -20
negative, NO solutions

6. 2 solutions 1 solution no solution 2 x-intercepts 1 x-intercept
The number of solutions tells you what the related parabola looks like.
CROSSER
TOUCHER
FLOATER/SINKER
2 solutions
1 solution
no solution
2 x-intercepts
1 x-intercept
no x-intercepts

7. Homework
pg # 1-20