Fit (2, 2), (6, 10), (10, 12), (16, 2) by a quadratic function (a2x2+ a1x+ a0=0).

Answer 1

There is no exact quadratic function that will satisfy all four of your points, so you will have to use some kind of "curve fitting".
You did not say at what level of math this is from, but if you are using a graphing calculator, most have a procedure that will perform this task.
Perhaps this will work for you ....
http://www.prenhall.com/divisions/esm/app/calc_v2/calculator/medialib/Technology/Documents/TI-82/desc_pages/quad-reg.html

if not, the following search might lead you in the right direction.
http://www.google.com/search?hl=en&rls=ig&biw=1659&bih=952&q=quadratic+equation+of+best+fit&aq=f&aqi=g-v1&aql=&oq=&gs_rfai=