Hello from MrBillDoesmath!
The questions are a bit unclear but here's my best shot
Answer:
a. "c" = 0
As x=0 is a root of f(x) = ax^2 + bx + c (I think this is the equation you had in mind. Please correct me if I'm wrong)
a(0)^2 + b(0) + c = f(0) = 0.
As any number times 0 is 0 this is equivalent to
0 + 0 + c = 0. So c = 0!
b. From part a (above) f(x) = ax^2 + bx. Suppose x is an extremely large number (positive or negative). If "a" is positive then f(x) is a large positive number so f(x) is large and looks like the letter "U". But if "a" is negative and x large (positive or negative), then f(x) is a large negative number, meaning the function looks like an upside-down "u". IN short, f(x) is a parabola that opens upward if a > 0 and opens downward if a < 0.
Given that f(x) = ax^2 + bx = x(ax+b), f(x) = 0 when x = 0 or (ax + b) = 0. The latter happens when ax = -b or x = - (b/a)
c. ax^2 + bx = 0
Ragards, Mr B.