Question 925668
you need to use the basic form of the equation that tells you that f(x) = ax^2 + bx + c


you now have 3 equations you can work with.

f(1) = a*1^2 + b*1 + c = 4
f(2) = a*2^2 + b*2 + c = 12
f(4) = a*4^2 + b*4 + c = 46


translate this to a system of 3 equations as follows:

1a + 1b + c = 4
4a + 2b + c = 12
16a + 4b + c = 46


these 3 equations have to be solved simultaneously for a, b, and c.
once you get that, you have your answer.


your answer will be:


a = 3
b = -1
c = 2


when you replace a,b, and c with those values, all the equations will be true.


1a + 1b + c = 4 becomes 1*3 + 1*-1 + 2 = 4 which becomes 3 - 1 + 2 = 4 which becomes 4 = 4 which is true.


4a + 2b + c = 12 becomes 4*3 + 2*-1 + 2 = 12 which becomes 12 - 2 + 2 = 12 which becomes 12 = 12 which is true.


16a + 4b + c = 46 becomes 16*3 + 4*-1 + 2 = 46 which becomes 48 - 4 + 2 = 46 which becomes 46 = 46 which is true.


all the values are good.


i'm assuming you know how to solve 3 equations simultaneously.
if you don't, let me know and i'll take you through that.