Question 960907: A cubic polynomial function f has leading coefficient 2 and constant term 7. If f(1)=7 and f(2)=9, what is f(-2)?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A cubic polynomial function f has leading coefficient 2 and constant term 7. If f(1)=7 and f(2)=9, what is f(-2)?
------
f(x) = ax^3 + bx^2 + cx + 7
----
Using f(1) = 7 you get: a + b + c + 7 = 7
Using f(2) = 9 you get: 8a+4b+2c + 7 = 9
------
Modify::
a + b + c = 0
4a + 2b + c = 1
-------------------------
Subtract to get:
3a + b = 1
----
Since a = 2, 6+b = 1
b = -5
---
Solve for "c"::
2 -5 + c = 0
c = 3
---------------
f(x) = 2x^3 -5x^2 + 3x + 7
-----------
Ans: f(-2) = -16-20-6+7 = -35
------------------
Cheers,
Stan H.
-------------
|
|
|
