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.
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)
x2 = 4py
(-18)2 = 4p(-18) p = -4.5
x2 = -18y
Now reread the problem. What is the critical point? When y = -8.
So… x2 = -18(-8)
Then x= 12ft