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CA STANDARDS
20.0: Students use the quadratic formula to find the roots of a
second-degree polynomial and to solve quadratic equations.
Learning Objectives: Given a quadratic equation, students
will be able to determine how many solutions it has.
Agenda
1.) Lesson On The Discriminant
2.) Assignment
The number of Solutions, Roots, X – Intercepts, and Zeros
depends on the value under the square root in the Quadratic
Formula!
b 4ac
2
Discriminant
If it is Negative
Then Zero (0) Solutions
If it is Positive
Then Two (2) Solutions
If it is Zero
Then One (1) Solution
2
Example 1: How many times does the graph of y 4 x 4 x 1
intersect the x-axis? b 2 4ac
4
a _____
4
b _____
(4)2 - 4(4)(1) 16 16
1
c _____
0
Therefore, there is One Solution
Example 2:
How many X-Intercepts does the graph of
y x 2 x 3 have?
b 2 4ac
(1)2 - 4(1)(3) 1 12
11
Therefore, there are No Solution
1
a _____
b _____
1
c _____
3
Example 3:
How many Solutions does the following equation have?
2
a _____
y 2x2 2x 2
b 2 4ac
(2)2 4(2)(2)
4 16 20
b _____
2
-2
c _____
Therefore, there are Two Solutions
You try:
How many Roots does the following equation have?
2 x2 4 x 2 0
b 2 4ac
2
(4) 4(2)(2)
a _____
2
-4
b _____
2
c _____
16 16 0
Therefore, there is One Solution