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.
I hope you can help me!!© BrainMass Inc. brainmass.com December 24, 2021, 4:52 pm ad1c9bdddf
SOLUTION This solution is FREE courtesy of BrainMass!
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 for exploring "d", get a graphing calculator and start changing the values of c and see what happens.
I hope this helps and take care.© BrainMass Inc. brainmass.com December 24, 2021, 4:52 pm ad1c9bdddf>