interesting derivative question

so i have a multipart question. the first is find the derivative of ax^2+bx+c, which i got to be 2ax+b.

the next part of the question reads the graph below is the graph of a function of the form f(x)=ax^2+bx+c. determine the sign of a, b, and c: positive , negative, or zero using the above derivative information. Answers without an explanation including the derivative will receive no credit.

the graph has a parabola opening up with intercepts at -2, 2. and a y int -4

so the c of the function is -4, i know that for sure, it was given that c was the y int of the parabola. i think that b of f prime is the y int of the tan line? so also -4? then i dont know what the a is. any help? as the question says i have to use the derivative to get the the values of a and b. this question is practice sheet is driving me nuts, and i want to see it through. ive just gotten so far (i think) id like to get it done. there are 9 other graphs on this sheet, so if someone could help me with this one, i could get the others. I just cant make the connection to what the sign of a is using the derivative.