1. Quadratic Formula & Discriminant

2. Vocabulary
Discriminant - tells you how many solutions and what type you will have.
If the discriminant is
positive – 2 real solutions
negative – 2 imaginary solutions
zero – 1 real solution

3. Notice where the discriminant is in the quadratic formula!
Formulas
Discriminant: b2-4ac
Quadratic formula – it is on the EOCT formula sheet
Notice where the discriminant is in the quadratic formula!

4. Examples 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

5. Using the quadratic formula
Make equation say = 0
Find the discriminant, take its square root
Plug a, b, c, and discriminant into formula
simplify

6. Examples - solve
3x2+8x=35
3x2+8x-35=0
a=3, b=8, c= -35 OR

7. -2x2=-2x+3
-2x2+2x-3=0
a=-2, b=2, c= -3

8. 3. 4x2+10x=-10x-25
4x2+20x+25=0
a=4, b=20, c=25