1. The Quadratic Formula & Discriminant
Essential question – How do you solve a quadratic equation using the Quadratic Formula?

2. When to use the quadratic formula:

3. Where does the formula come from?

4. Discriminant: b2-4ac
The discriminant tells you how many solutions and what type you will have.
If the discriminant b2-4ac
Is positive, there are 2 real solutions
(2 x-intercepts)
Is negative, there are 2 imaginary solutions
(0 x-intercepts)
Is zero, there is 1 real solution (double root!)
(1 x-intercept)

5. 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

6. Quadratic Formula (it has a song!)
Notice where the discriminant is in the quadratic formula!

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

8. -2x2=-2x+3
-2x2+2x-3=0
a=-2, b=2, c= -3

9. 3. 4x2+10x=-10x-25
4x2+20x+25=0
a=4, b=20, c=25

10. Now you try…
p. 117, #2-16 even
HW: p. 117, #18-54 multiples of 3