Question

A tunnel is in the shape of a parabola. The maximum height is 50 m and it is 10 m wide at the base as shown below.

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What is the vertical clearance 2 m from the edge of the tunnel?

Answer 1

I would find the equation of the parabola, then use that equation with x=8 (which is 2 m from the edge at x=10)

Answer 2

the zeros of this parabola are at x=10 and x=-10 (with x=0 the middle of the parbola)
in other words,
y = a(x-10)(x+10)
where we still need to find a

luckily we know when x=0 the parabola has height 50 (i.e. y=50)
so put in x=0 and y=50:

50 = a(-10)(+10)
50 = a* -100
divide both sides by -100
-1/2 = a

and the equation is
\[ y= - \frac{1}{2} (x-10)(x+10) \]

Answer 3

After posting all of that , I see the zeros are at x=5 and x=-5

oops. but hopefully you can redo the work and get the correct equation??

the zeros of this parabola are at x=5and x=-5 (with x=0 the middle of the parbola) in other words,

y = a(x-5)(x+5) where we still need to find a

Answer 4

a= -2

Answer 5

yes, and the equation is
y = -2 (x-5)(x+5)

and 2 meters in from the edge (at x=5) would be x=3 (or x=-3)
so put in x= 3 into the equation and find y

Answer 6

y=32

Answer 7

that is what I got.

Answer 8

So is that the answer?

Answer 9

yes

Answer 10

thanks :)