Cubic Functions

Date: 5/13/96 at 23:48:59
From: Anonymous
Subject: Cubic Functions

Hi there! I hope you can help me with my problem.

Investigate the cubic functions of f(x) = ax^3 + bx^2 + cx + d 
which will pass through the points of A = (1,4) B = (2,2) C = (4, 1.5)

Now explore the effect of 'd' on the behaviour of the cubic functions.  
Identify a value of 'd' that gives a cubic function which closely 
matches the quartic function that passes through these same three 
points (A,B,C).  You will need to explain how you have measured 
'closely', paying particular attention to the domain.

There you have it... I hope you can help me!!

Thank you,
Matt

Date: 11/12/96 at 21:50:55
From: Doctor Robert
Subject: Re: Cubic Functions

You can find the function by substituting the ordered pairs into the 
general equation for a cubic (which you have shown). You get:

  4 = a + b + c
  2 = 4a + 2b + c
  1.5 = 16a + 4b + c

Solve this system for values of a, b, and c. Then get a graphing 
calculator and start changing the values of c and see what happens.

-Doctor Robert,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/