Question

Lindsay is creating a bridge out of dried pasta and glue. In her plans, she sketches the graph to determine the lengths of the noodles, in centimeters, needed for the arch to increase the length of the bridge in 1-centimeter increments.

A graph shows distance from left (centimeters) labeled 1 to 10 on the horizontal axis and length of noodle (centimeters) on the vertical axis. A line increases from 1 to 5 then decreases from 5 to 9.

Which function did Lindsay use to create her design?

f(x) = (x – 5)2 + 8
f(x) = –(x + 5)2 + 8
f(x) = 0.5(x + 5)2 + 8
f(x) = –0.5(x – 5)2 + 8

Answer 1

Answer: f(x) = –0.5(x – 5)^2 + 8.

Reason: The graph has a maximum (vertex) at x = 5 with value 8 and is concave down. Only f(x) = –0.5(x – 5)^2 + 8 has vertex (5,8) and opens downward; it also gives f(1)=f(9)=0, matching the rise from x=1 to 5 and fall from 5 to 9.