## 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

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 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?

## Answers ( No )

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.