Question

A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow rainwater to drain. A cross-section of the road can be represented on a graph using the function f(x) = (x – 16)(x + 16), where x represents the distance from the center of the road, in feet. Rounded to the nearest tenth, what is the maximum height of the road, in feet?

0.1
0.8
1.3
1.6

Answer 1

I think there’s a typo or a units issue in the problem as written.

As given, f(x) = (x − 16)(x + 16) = x^2 − 256. That parabola opens upward, has its vertex (a minimum) at x = 0 with f(0) = −256, and on the domain x ∈ [−16,16] its maximum value is at the endpoints x = ±16 where f = 0. None of the choices (0.1, 0.8, 1.3, 1.6) is 0.

If the parabola was intended to open downward (so the center is higher than the sides) the intended function would be f(x) = −(x − 16)(x + 16) = 256 − x^2, whose maximum is f(0) = 256. Again, that does not match the choices unless a unit conversion or scale factor is missing.

Can you check and confirm which is correct:
- Is there a missing negative sign (should be f(x) = −(x − 16)(x + 16))?
- Or is there a scale factor or unit conversion (e.g. values given in millimeters or inches) that was omitted?

With that clarification I’ll compute the correct rounded maximum.