Problem Solving

7. A 10ft high truck passes under a parabolic arch. Find the maximum distance x that the side of the truck can be from the center of the road.

NEED SKETCH

Solution:

First set the reference axes at a convenient location. I chose the top of the arch.

Next write the equation for the parabola. Use the point (-18, -18)

x^{2} = 4py

(-18)^{2} = 4p(-18) p = -4.5

x^{2} = -18y

Now reread the problem. What is the critical point? When y = -8.

So… x^{2} = -18(-8)

Then x= 12ft