1. The Discriminant

2. The DISCRIMINANT (the part of the quadratic equation underneath the radical) will help you to predict the number of solutions any quadratic equation has.
If the DISCRIMINANT is:
positive there will be 2 solutions
negative there will be NO solution
zero there will be 1 solution

3. positive negative zero
discriminant
negative
zero
x2 – 5x + 2 = 0
2x2 + x + 3 = 0
x2 + 6x + 9 = 0
b2 – 4ac = (-5)2 - 4(1)(2)
b2 – 4ac = (1)2 - 4(2)(3)
b2 – 4ac = (6)2 - 4(1)(9)
undefined
2 real roots
0 real roots
1 real root
double root

4. positive discriminant:
Find the value of the discriminant. Then use the value to determine whether the equation has two solutions, one solution or no real solution.
negative discriminant: no real solution
zero discriminant: one solution
positive discriminant:
two solutions

5. positive discriminant:
Determine the number of x-intercepts (two, one or none) of the graph of the function without graphing.
positive discriminant:
2 x-intercepts
negative discriminant: no x-intercepts
zero discriminant: x-intercept

6. Without graphing, determine the x-intercepts of the graph of each function:
These problems ask for the actual x-intercepts, but you can save time using the discriminant first.
b2-4ac
b2-4ac
Since discriminant is positive, finish solving quad. formula
Since discriminant is negative, stop solving, there is no solution.

7. Without graphing, determine the x-intercepts of the graph of each function:
b2-4ac
b2-4ac
Since discriminant is zero, you will have ONE solution
Since discriminant is positive, finish solving quad. formula

8. which we will get to tomorrow,
In word problems,
which we will get to tomorrow,
if you are asked if something is possible,
that means find the discriminant.
If it is positive or zero, then it is possible.
If it is negative,
then it is not possible because it would be no solution.
We will get into more word problems tomorrow.