Can someone me with this math question? i am assume that f(x) = ax^2 bx + c has real roots at x = 0 and at another, non-zero value. a. what must the numeric value of c be? explain your reasoning. b. sketch a possible graph of f(x) on the coordinate plane. indicate the coordinates of the roots on your graph. c. determine the equation in standard form for the function graphed?

Hello from MrBillDoesmath!

The questions are a bit unclear but here's my best shot

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.