1. 5.6 Quadratic Formula & Discriminant

2. Discriminant: b2-4ac
The discriminant tells you how many solutions and what type you will have.
If the discriminant:
Is positive – 2 real solutions
Is negative – 2 imaginary solutions
Is zero – 1 real solution

3. 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

4. Quadratic Formula (Yes, it’s the one with the song!)
If you take a quadratic equation in standard form (ax2+bx+c=0), and you complete the square, you will get the quadratic formula!

5. When to use the 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.)

6. Examples
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