7-2 Identifying Functions from Graphical Patterns

Overview:

Linear:
general: y=ax+b
parent: y=ax
transformed: y-y1=a(x-x1)


Quadratic:
general: y=ax^2 + bx+c
parent: y=x^2
transformed: y-k = a(x-h)^2


Power:
general: y = ax^b
parent: y=x^b
transformed: y=a(x-c)^b + d


Exponential:
general: y=ab^x
parent: y=b^x
transformed: y=ab^(x-c)+d

If you are given x and y in a quadratic funtion and required to find a, b, and c use matrices.
To find slope its rise/run

Practice Problem:

Find a, b, c for the following quadratic equation if (1,-7) (2,0) (3,9)
use matrices
[1 , 1 , 1 ]-1 [-7 ] [ 1 ]
[4 , 2 , 1] times [ 0 ] = [ 4 ]
[9 , 3 , 1] [ 9 ] [-12] so a=1, b=4, c=-12

y=x^2 +4x -12

Other Material
http://library.thinkquest.org/2647/algebra/functype.htm

This is one of the funniest SNL skits i've seen in a long time. I'm sure everybody has watched SNL at one point or another so I think that this is appropriate.
http://youtube.com/watch?v=1dmVU08zVpA