CA STANDARDS20.0: Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.

AgendaAgenda

1.) Lesson On The Discriminant

2.) Assignment

Learning Objectives: Given a quadratic equation, students will be able to determine how many solutions it has.

The number of Solutions, Roots, X – Intercepts, and Zeros depends on the value under the square root in the Quadratic Formula!

If it is Negative Then Zero (0) SolutionsThen Zero (0) Solutions

If it is Positive Then Two (2) SolutionsThen Two (2) Solutions

If it is Zero Then One (1) SolutionThen One (1) Solution

2 4b ac

Example 1:

_____a_____b_____c

441

2 4b ac

16 16 0

Therefore, there is One Solution

Discriminant

24 4 1y x x How many times does the graph of intersect the x-axis?

Example 2:

How many X-Intercepts does the graph of have? 2 3y x x

_____a_____b_____c

113

2 4b ac

1 12 11

Therefore, there are No Solution

22 2 2y x x _____a_____b_____c

2

2

-2

2 4b ac2(2) 4(2)( 2) 4 16 20

Therefore, there are Two Solutions

How many Solutions does the following equation have?

22 4 2 0x x _____a_____b_____c

2

-4

2

2 4b ac2( 4) 4(2)(2)

16 16 0Therefore, there is One Solution

How many Roots does the following equation have?

Example 3:

You try: