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

3. When to use the quadratic formula:

4. Where does the formula come from?

5. Discriminant: b 2 -4ac The discriminant tells you how many solutions and what type you will have. If the discriminant b 2 -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)

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

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

8. Examples 1. 3x 2 +8x=35 3x 2 +8x-35=0 a=3, b=8, c= -35 OR

9. 2. -2x 2 =-2x+3 -2x 2 +2x-3=0 a=-2, b=2, c= -3

10. 3. 4x 2 +10x=-10x-25 4x 2 +20x+25=0 a=4, b=20, c=25

11. Now you try… p. 117, #2-16 even