Question

A graph with both axes numbered 1 to 10. A line increases from 1 to 3 then decreases from 3 to 5.
What function models the data shown on the graph?

f(x) = 2(x – 5)(x – 1)
f(x) = –2(x – 5)(x – 1)
f(x) = 2(x + 5)(x + 1)
f(x) = –2(x + 5)(x + 1)

Answer 1

Choose f(x) = –2(x – 5)(x – 1).

Reason: the graph has zeros at x = 1 and x = 5 and reaches a maximum at x = 3 (increases to 3 then decreases), so the parabola opens downward and factors are (x−1)(x−5). The negative leading coefficient option is –2(x−5)(x−1).