How do you find a quadratic model?

1 Answer
Mar 22, 2015

How you establish a quadratic model depends upon what information you have available.
Probably the easiest way to find a quadratic model is if you are given #3# points #(p_1,q_1), (p_2,q_2), (p_3,q_3)# which satisfy the quadratic model.

A quadratic can be expressed as:
#ax^2 + bx + c#

With #3# points we can write #3# equations with #a, b, c# as variables:
#a(p_1)^2 + b(p_1) + c = q_1#
#a(p_2)^2 + b(p_2) +c = q_2#
#a(p_3)^2 + b(p_3) + c = q_3#
which can then be solved for #a,b,# and #c#.

For example if the points are:
#(1,-1), (4,-1),# and #(5,3)#
the equations are
#1*a + 1*b + c = -1#
#16*a + 4*b + c = -1#
#25*a + 5*b + c = 3#
which can be solved for
#a=1#, #b=-5#, and #c=3#
for a quadratic model
#x^2 - 5x + 3#