The height above water level of a curved arch for a bridge can be modeled by h(x) = -0.009x^2 + 1.08x − 0.4, where x is the distancein feet from the point where the left leg of the arch is planted in the ground.

Question

A boat traveling under the arch is 26.5 feet tall. What is the vertical distance between the tallest point on the boat and the tallest point on the arch as the boat passes under the bridge?

~I got 33.5 doing the problem and i got it wrong can you please explain it to me and help me

Answer 1

where is the vertex of that parabola?

You do not say if you know calculus so I will assume we do it the hard way with algebra

.009 x^2 -1.08 x = -h -.4
x^2 - 120 x = -111h - 44.4
x^2 -120 x + 3600 = -111h + 3556
(x-36)^2 = -111(h-32)
vertex at x = 36 and h = 32
32 -26.5 = 5.5

Answer 2

Thank's for helping me.

Answer 3

You are welcome.