SOLUTION: Find the function ​f(x)=ax^3+bx^2+cx+d for which, f(-3)=-83, f(-1)=1, f(1)=5, f(2)=7.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Find the function ​f(x)=ax^3+bx^2+cx+d for which, f(-3)=-83, f(-1)=1, f(1)=5, f(2)=7.      Log On


   

Question 1155341: Find the function ​f(x)=ax^3+bx^2+cx+d for which, f(-3)=-83, f(-1)=1, f(1)=5, f(2)=7.
Found 4 solutions by Edwin McCravy, mananth, MathTherapy, ikleyn:
Answer by Edwin McCravy(20063) About Me  (Show Source):
You can put this solution on YOUR website!
Find the function ​f(x)=ax^3+bx^2+cx+d for which, f(-3)=-83, f(-1)=1, f(1)=5,
f(2)=7.



That simplifies to this system of equations:



Solve that system either by elimination or 
matrix methods.

a=2, b=-4, c=0, d=7

So:

matrix%281%2C3%2C%22f%28x%29%22%2C%22%22=%22%22%2Cax%5E3%2Bbx%5E2%2Bcx%2Bd%29

becomes:

matrix%281%2C3%2C%22f%28x%29%22%2C%22%22=%22%22%2C2x%5E3-4x%5E2%2B0x%2B7%29

We drop the 0x term:

matrix%281%2C3%2C%22f%28x%29%22%2C%22%22=%22%22%2C2x%5E3-4x%5E2%2B7%29

Edwin

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
f(x)=ax^3+bx^2+cx+d

f(1)=> a+b+c+d =5
F(2)=> 8a +4b+2c+d =7
f(-1)=> =-a +b -c +d = 1
f(-3)=> -27a +9b -3c +d =-83
use calc
to get a=-2.5,b=-3,c=-2.5,d=4
plug valuea to get function

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Find the function ​f(x)=ax^3+bx^2+cx+d for which, f(-3)=-83, f(-1)=1, f(1)=5, f(2)=7.
Do NOT plug in mananth's values for a, b, c, and d. They're simply WRONG!!

Answer by ikleyn(52866) About Me  (Show Source):
You can put this solution on YOUR website!
.

Dear tutor @mananth,

it looks like you need a special helper, who will check after you.


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Not every student in high school is able to solve 4x4 matrix equation manually.

Even with simplifying which goes from +1 and -1 in arguments, it is difficult treat for an average student.

Therefore, I think that the meaning of this problem is to get the system of equations for 4 unknown coefficients,
and then solve it (almost mechanically) using a pocket calculator and its matrix functions / solvers.