Question

All-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

f(x) = –4(x – 50)(x – 250)

Reason: the table gives zeros at x = 50 and x = 250, so factors (x−50)(x−250) are needed. Monthly profit peaks between those zeros, so the parabola opens downward — the only choice with a negative leading coefficient is −4(x−50)(x−250).