Question

ll-Star Trinkets estimates its monthly profits using a quadratic function. The table shows the total profit as a function of the number of trinkets produced.


Which function can be used to model the monthly profit for x trinkets produced?

f(x) = –4(x – 50)(x – 250)
f(x) = (x – 50)(x – 250)
f(x) = 28(x + 50)(x + 250)
f(x) = (x + 50)(x + 250)

Answer 1

I don’t see the table you mentioned — could you paste the values (profit for some x)? With those I can pick which function is correct.

How you (or I) would choose among the four options:
- From the table find the x-values where profit = 0. Those give the roots; they tell you whether the factors should be (x − 50)(x − 250) or (x + 50)(x + 250).
- Use one nonzero data point (x0, f(x0)) to solve for the leading coefficient a by plugging into a(x0 − r1)(x0 − r2) = f(x0).
- The sign of a is determined by whether the parabola opens up (a > 0) or down (a < 0), which you can tell from the table (profits drop off for large or small x means negative a).

Example: if the table shows zeros at x = 50 and x = 250 and f(150) = 40,000, then
a(150−50)(150−250) = 40,000 → a(100)(-100) = 40,000 → -10,000a = 40,000 → a = -4,
so f(x) = −4(x − 50)(x − 250) (the first choice).

Send the table and I’ll confirm which option matches.