9.5 Problem Solving using the
Discriminant
Homework
Any Questions?
What is the quadratic formula?
 b  b 2  4ac
x
2a
When you get the answer to the equation, what does it
tell you?
Where is crosses the x-axis
In the quadratic equation, b2 – 4ac is called the
discriminant. The discriminant can tell you some unique
information…
it can tell you how many answers to the equation
(places it crosses the x-axis)
Number of Solutions for a Quadratic Equation
1. If b2 – 4ac is positive, then the equation has 2 solutions or it
crosses the x-axis at two places.
2. If b2 – 4ac is zero, then the equation has only one solution
or the vertex is on the x-axis.
3. If b2 – 4ac is negative, then the equation has no solutions or
it never crosses the x-axis.
Example 1: Checking for the number of solutions
A. x2 -2x + 3 = 0
a=1
b = -2
c=3
b2 – 4ac = (-2)2 – 4(1)(3)
= 4 – 12 = -8
therefore, the equation has no solutions
Cool Fact of the Day
Cast iron skillets used to
be the leading source of
iron in the American diet.
5
B.
x2 – 2x + 1 = 0
b2 – 4ac = (-2)2 – 4(1)(1) = 0
One solution
C. x2 - 2x – 2 = 0
b2 – 4ac = (-2)2 – 4(1)(-2) = 12
Two Solutions
Practice
Decide how many solutions the equation has
Homework
Pg. 483 #4-13