Question

Would a truck that is 12 feet tall and 9 feet wide fit through a parabolic arch that is 15 feet high at the high point and 16 feet wide?

Answer 1

let the vertex be (0,15)
then the equation is
y = ax^2 + 15
the x-intercept is (8,0)
0 = 64a + 15
a = -15/64

y = (-15/64)x^2 + 15

so when x = 4.5 , assuming the truck goes down the middle of the road
y = (-15/64)(4.5^2) + 15
= 10.25

but the truck is 12 ft tall, so it can't pass through the arch