SOLUTION: Find the function f(x)=ax^3+bx^2+cx+d for which f(0)=-2, f(1)=5, f(-1)=3, f(2)=4

Algebra ->  Rational-functions -> SOLUTION: Find the function f(x)=ax^3+bx^2+cx+d for which f(0)=-2, f(1)=5, f(-1)=3, f(2)=4      Log On


   

Question 935800: Find the function f(x)=ax^3+bx^2+cx+d for which f(0)=-2, f(1)=5, f(-1)=3, f(2)=4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find the function f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd for which f%280%29=-2, f%281%29=5, f%28-1%29=3, f%282%29=4:
f%28x%29=ax%5E3%2Bbx%5E2%2Bcx%2Bd....we need to find coefficients
f%280%29=-2
f%280%29=a%2A0%5E3%2Bb%2A0%5E2%2Bc%2A0-2=> highlight%28d=-2%29

f%281%29=5
5=a%2A1%5E3%2Bb%2A1%5E2%2Bc%2A1-2
5%2B2=a%2Bb%2Bc
a%2Bb%2Bc=7..................eq.1

f%28-1%29=3
3=a%2A%28-1%29%5E3%2Bb%2A%28-1%29%5E2%2Bc%2A%28-1%29-2
3%2B2=-a%2Bb-c
-a%2Bb-c=5..................eq.2

f%282%29=4
4=a%2A2%5E3%2Bb%2A2%5E2%2Bc%2A2-2
4%2B2=8a%2B4b%2B2c
6=8a%2B4b%2B2c
3=4a%2B2b%2Bc
4a%2B2b%2Bc=3..................eq.3

use eq.1 and 2
a%2Bb%2Bc=7..................eq.1
-a%2Bb-c=5..................eq.2
------------------------------------add both
a%2Bb%2Bc-a%2Bb-c=7%2B5
2b=12
highlight%28b=6%29
go to 4a%2B2b%2Bc=3..................eq.3 substitute b
4a%2B2%2A6%2Bc=3
4a%2B12%2Bc=3...solve for c
c=3-4a-12
c=-4a-9....->
go to a%2Bb%2Bc=7..................eq.1 substitute b and c
a%2B6-4a-9=7.....solve for a
-3a-3=7
-3a=7%2B3
highlight%28a=-10%2F3%29
then c=-4a-9
c=-4%28-10%2F3%29-9
c=40%2F3-27%2F3
highlight%28c=13%2F3%29

the function is: f%28x%29=-%2810%2F3%29x%5E3%2B6x%5E2%2B%2813%2F3%29x-2