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### 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/
```
Associated Topics:
College Modern Algebra
High School Basic Algebra

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