Partially Preposterous Parabolic Perplexing Problem

Let's see, f(1) = 43 = a(1²) + b(1) + c = a + b + c.

Plugging it in -_-. Origin is (0,0), so plug it in the quadratic so that it looks like $a(0) + b(0) + c = 0$ $c = 0$

Now use (1,43) and use the knowledge that $c = 0$ , so that $a(1^2) + b(1) + 0 = 43$ $a + b = 43$

Now you have the answer: $a+b = 43, c = 0$ , so $a+b+c=\boxed{43} \textbf{ Ans.}$