A function is simply a rule that tells you how to associate every (feasible) input with its correspondant output. So, in this case, your function/rule of association is
[tex] \displaystyle f(p) = p^2+3p+1 [/tex]
which can be read as:
"Given any number [tex] \displaystyle p [/tex], the correspondant output is that same number squared, plus three times that number itself, plus one".
This rule holds for every possible input [tex] \displaystyle p [/tex], and of course the result will change depending on which input you will feed the function.
In this case, we're interested in feeding the function the number [tex] \displaystyle -2 [/tex]. Let's use the verbose definition first, to understand better what's happening. It translates to
"Given the input [tex] \displaystyle -2 [/tex], the correspondant output is negative two squared, plus three times negative two, plus one".
Which, in formula, is written as
[tex] \displaystyle f(-2) = (-2)^2 + 3(-2) + 1 = 4-6+1 = -1 [/tex]
