1. 4.8 Use the Quadratic Formula & the Discriminant
Algebra II

2. 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!

3. 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.)

4. Example
3x2+8x=35
3x2+8x-35=0
a=3, b=8, c= -35 OR

5. -2x2=-2x+3
-2x2+2x-3=0
a=-2, b=2, c= -3

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

7. Example 3 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

8. Assignment