Question 750632: A parabola shaped tunnel is 10m high at the centre and spans 18m wide at the base. A 7.5 m high vehicle needs to use the tunnel;, what is the maximum width of the vehicle that can fit through the tunnel?
I need to draw a diagram to represent the tunnel on a coordinate number plane , and find the equation of the parabola. using algebra and coordinate geometry to determinate the maximum width of the truck
I try to solve this problem many times but my results seems to be wrong, please help me I'm so stuck
Ally
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! Start this way:
The x-axis would be the road along its width. The center line of the road would be where x=0, so the center of the road is the axis of symmetry for the parabola. The vertex is at y=10 and x=0. From the center line of the road to either side is a length half of 18 meters, or 9 meters. This means, the zeros on the graph are (-9,0) and (9,0). Obviously the graph has a maximum point and this parabola opens downward.
That will help in sketching the graph. You want the equation for this parabola so you can use it to find the values about the truck to pass through the tunnel. What can be done so far? Seeing the graph may help.
Standard Form will also help.  ,
vertex is (h,k), and the zeros will help with finding 'a'.
Use (-9,0).
 , and the use of (9,0) will give the same value for a.
The equation seems to be  . I leave the job of finding the truck width to you.
Check to see that you made a graph agreeable to this:
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