Tunnel math problem

[whynot]

Hi there! I just started this problem but I keep getting negative answers (which I don't think it's right) My teacher had done one but this one is quite different:

The Moving Transportation Committee has proposed to build an underground tunnel between Scarborough and Mississauga to help ease a lot of traffic woes.
The proposed tunnel will consist of two driving lanes and is to be built in the shape of a parabolic arch, with its base 12 m wide and its highest point 5 m above ground.

As the Math Analyst, your task is to determine the “Maximum Height Allowed” for the vehicles that are passing through this tunnel and a justification to how this “maximum height” was determined.

I tried using h(x)=a(x+6)(x-6) as my first step - because the total base is 12 divided by 2 gives negative 6 and positive 6, so...
5=a(0+6)(0-6)
5=- 36a ..............................[edited]
-5/36=a .............................[edited]
that is the equation I used for the next step, I sub the points (0,5) because those are the height points but i'm still confused - so for one answer i got -4.19
I know everything might be incorrect but I'm not sure how to start

 

[Romsek]

Since the parabola is pointed downwards, i.e. the vertex is the maximum point, it must be that [MATH]a[/MATH] is negative.

Try again with [MATH]a=-\dfrac{5}{36}[/MATH]
You're going to need to select how much shoulder room you're going to have on each side of the tunnel.
Then find out what the height of the arch above the ground is at the edge of the shoulders. That will be the lowest point on the arch that the traffic might intersect.

 

[Steven G]

Please try not to say that 12 divided by 2 is 6 and -6. You know that 12/2 is 6 and not -6. Just try to word that sentence better.