1. The Discriminant
  Determine the number of real solutions for a quadratic equation including using the discriminant and its graph.

2. Using the Discriminant
In the Quadratic Formula, the expression under the radical sign, b2-4ac
is called the discriminant! The value of the discriminant can be used to determine the number of real roots for a quadratic equation!

3. Plug these in the formula!
Using the formula!
2x2 + 10x +11 =0
a=2, b=10, c=11
Plug these in the formula!
b2 - 4 a c
(10)2-4(2)(11)
Use your calculator for this step!
Therefore the discriminant is 12

4. How to know how many roots or solutions a quadratic equation has by using the discriminant and looking at a graph
y=2x2+x+3
2x2+x+3=0
b2-4ac
(1)2-4(2)(3)
= -23
If the answer is negative you will have 0 Real roots
If the graph does not cross the x-axis you will have 0 roots!

5. Example x2+6x+9=0 b2-4ac y=x2+6x+9 (6)2-4(1)(9) The answer is 0.
When the answer is zero you will have 1 real root!
y=x2+6x+9
The graph touches the x-axis in one place. We call this a double root!

6. Example x2-5x+2=0 b2-4ac (-5)2-4(1)(2) The answer is 17
Since the answer is positive you will have 2 real roots!
The graph crosses the x-axis twice!