A highway tunnel has a shape that can be modelled by the equation of a parabola. The tunnel is 18 m wide and the height of the tunnel 16 m from the edge is 5 m.

Question

Question #1:

Question #2:

A highway tunnel has a shape that can be modelled by the equation of a parabola. The tunnel is 18 m wide and the height of the tunnel 16 m from the edge is 5 m.

a) Determine the equation of the parabola.

b) Sketch a graph of your parabola. Capture your work and insert the image or link here. :)

c) Can a truck that is 8 m tall and 4 m wide pass through the tunnel? Justify your decision.

Answer 1

graph the parabola with axis of symmetry x=0, x intercepts x=9 and -9,

height of the tunnel is 16 meters? or 16 meters from top of the tunnel to an edge of the bottom?

if the former, the y intercept = 16 and the vertex is (0, 16)

the equation is y=a(x-9)(x+9) = a(x^2 -81) where a<0

to find a plug in the point (0,16)

16 =-a81

a =-16/81

the equation is y = (-16/81)(x^2 -81)

or y = (-16/81)x^2 + 16

if the truck is 4 meters wide, graph its x coordinates as -2 and 2, if it drives down the center of the tunnel's road.

then find y(2) = (-16/81)(2^2) +16 = -64/81 + 16 = 15.21 meters is high enough for a 8 meter high truck

but if the truck goes down only a right lane, right of center, graph the x coordinates of the truck as 0 and 4

y(4) = (-16/81)(4^2) + 16 = -256/81 +16 = 12.84 meters also high enough for the 8 meter high truck to pass through.