1. 5.6 Quadratic Formula & Discriminant
OBJ: To find the discriminant & tell how many (and what type) of solutions there are & to a quadratic equation solve quadratic equations using the quadratic formula & use the quadratic formula in real-life situations
5.6 Quadratic Formula & Discriminant
Do Now:

2. Discriminant b2 - 4ac
The discriminant tells you how many solutions and what type you will have.
If it is:
positive, there are 2 real solutions
negative, there are 2 imaginary solutions
zero, there is 1 real solution

3. Ex 1: 9x2+6x-4=0 a=9, b=6, c=-4 b2-4ac=(6)2-4(9)(-4) =36+144=180
2 real solutions
c. 9x2+6x+5=0
a=9, b=6, c=5
b2-4ac=(6)2-4(9)(5)
=36-180=-144
2 imaginary solutions
Find the discriminant and give the number and type of solutions.
9x2+6x+1=0
a=9, b=6, c=1
b2-4ac=(6)2-4(9)(1)
=36-36=0
1 real solution

4. Quadratic Formula
Use the quadratic formula when you can’t factor to solve a quadratic equation.
(or when you’re stuck on how to factor the equation)

5. Ex 2:
a. 3x2+8x=35
3x2+8x-35=0
a=3, b=8, c= -35 OR

6. b. -2x2=-2x+3
-2x2+2x-3=0
a=-2, b=2, c= -3