1. YES! The Quadratic Formula
Lesson #21
The Quadratic Formula
YES! The Quadratic Formula

2. Recall that
1.The solution when y =0 from factored form y=a(x-z1)(x-z2)
2.The solution when y =0 from standard form y=a(x-h)2 +k
When the quadratic function is in
General form,
y = ax2 +bx + c
and cannot be factored easily (answers are square roots) use the……..
QUADRATIC FORMULA

3. Ex. 1 Case II: 1 zero Case 1. 2 zeros y = x2 + 2x + 1
Find the zeros
Case 1. 2 zeros
Case II: 1 zero
y = 5x2 + 20x - 30
y = x2 + 2x + 1

4. a a 4a2 2a 4a2 4a2 2a 4a2 2a 2a 2a 2a y = ax2 + bx + c
1. General formula
y = a(x2 + bx + c) a
2. Factor out the a
y = a(x2 + bx + b2 a
4a2
+ c)
- b2
3. Make a perfect square trinomial
y = a((x + b )2
- b2
+ 4a2c)
4. Factor and get a common
denominator 2a
4a2
4a2
y = a((x + b )2
- b2 + 4a2c )
5. Add the numerators 2a
4a2
0 = a(x + b )2 -b2 + 4ac
6. Multiply the a in 2a 4a
(x + b )2 = b2 - 4ac
7. Move term to other side of equal sign and divide by a 2a
4a2
(x + b ) = b2 - 4ac
8. –b/2a on both sides 2a 4a
x = -b b2 - 4ac
9. Final formula 2a

5. Homework
Handout #1-15