Help me! "How many quadratic fcns of x have graph passing thru at least 3 of marked pts?"

First, it has to be a function; what does that imply? Given that, any three non-collinear points determine a parabola. So you might count all ways to choose three points, and subtract the number of those that are collinear.

For further help, be sure to show your own work, so we have a place to start.
 
We have 9 choices for the first point, and then given we're talking about functions, how many choices do we have for the 2nd and 3rd points? For a given valid set of 3 points, how many ways can we order them? How many of these sets will be collinear?
 
I'd count the ways to choose f(1), f(2), and f(3), and then subtract all the linear functions (horizontal or diagonal lines).
 
As Dr Peterson has been saying it is best to do (3c1)3 - colinear triples
 
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