Find possible formulas for polynomials with the given properties.
a) f has degree ≤2, f(0) = f(1) = f(2) = 1.
b) f is third degree with f(-3) = 0, f(1) = 0, f(4) = 0 and f(2) = 5.
For a) I know that x values 0, 1, and 2 have y values of 1. These points should look like their in a straight formation. But how we find the formula for this? And what about b)?
Please explain and show me the process to solving these problems. Thanks.
The possible formulas for this is clearly f(x)=1
If you want to show it mathematically ,
Assume that f is of degree 2 , f(x)=ax^2+bx+c
Find f(0) , f(1) and f(2) , all =1 , then you will have a system simultaneous equations , solve it and you will find that a=0 , b=0 and c=1 .