## Can someone please help me with this math question? I am desperate!! Assume that f(x) = ax^2 bx + c has real roots at x = 0 and

Question

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?

0

1. 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.