Solving quadratic equation by quadratic formula

Discussion on quadratic formula

1. Intro:We already know the
standard form of a quadratic
equation is:
y = ax
2
+ bx + c
The coefficients are: a , b, c
The variablesare: y, x

2. The ROOTS(or
solutions) of a
polynomial are
its x-intercepts
The x-intercepts
occur where y =
0.Roots

3. Example:Find the
roots: y = x
2
+ x -6
Solution:Factoring:
y = (x + 3)(x -2)
0 = (x + 3)(x -2)
The roots are:
x = -3; x = 2Roots

4. After centuries of
work,
mathematicians
realized that as long
as you know the
coefficients, you can
find the roots of the
quadratic. Even if it
doesn’t factor! yax
2
bxc, a0
x
bb
2
4ac
2a

5. Solve: y=5x
2
8x3 x
bb
2
4ac
2a a5, b8, c3 x
(8)(8)
2
4(5)(3)
2(5) x
86460
10 x
84
10 x
82
10

6. x
82
10 x
82
10

10
10
1 x
82
10

6
10

3
5 Roots

7. y5(1)
2
8(1)3 y583 y0 y5
3
5
2
8
3
53 y5
9
25
24
53 y
45
25
24
53 y
9
5
24
5
15
5 y0 Plug in your
answers for x.
If you’re right,
you’ll get y = 0.

8. Solve: y2x
2
7x4 a2, b7, c4 x
bb
2
4ac
2a x
(7)(7)
2
4(2)(4)
2(2) x
74932
4 x
781
4 x
79
4 x
2
4

1
2 x
16
4
4

9. Remember: All the terms must be on one
sideBEFORE you use the quadratic
formula.
•Example:Solve 3m
2
-8 = 10m
•Solution:3m
2
-10m -8 = 0
•a = 3, b = -10, c = -8

10. Solve:3x
2
= 7 -2x
Solution:3x
2
+ 2x -7 =
0
a = 3, b = 2, c = -7x
bb
2
4ac
2a x
(2)(2)
2
4(3)(7)
2(3) x
2484
6 x
288
6 x
24•22
6 x
2222
6 x
122
3

11. Watch this:
http://www.youtube.com/watch?v=jGJrH49Z2ZA