Question

Can anyone please help me with this:

Answer 1

A tunnel is in the shape of a parabola. The maximum height is 16 m and it is 16 m wide at the base as shown below.

A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 16 meters and its width from left to right is 16 meters.

What is the vertical clearance 7 m from the edge of the tunnel?

Answer 2

Please help me :)

Answer 3

@ChristopherToni

Answer 4

would it be 7?

Answer 5

What does " 7 m from the edge " mean?

Answer 6

that it has to move from 8,0 on 7

Answer 7

You must find the equation of the parabola.

\(y - 16 = Ax^{2}\) <== How to find the value of "A"?

Answer 8

but how do i find a?

Answer 9

would y be 16 because the height is 16?

Answer 10

I put the Origin in the middle of the road. This makes the Vertex (0,16).

Put one of the other points (maybe (8,0)) in the equation and solve for A.

Answer 11

im not understanding what im supposed to do

Answer 12

Do you believe \(y - 16 = Ax^{2}\)

Answer 13

im not sure what you mean

Answer 14

We need the equation of that parabola. Is that it or not?

Answer 15

well i use this : (x-h)^2=4p(y-k) that's for vertical and horizontal is : (y-k)^2=4p(x-h ) @tkhunny

Answer 16

Okay, that's fine. We know the vertex is (0,16). Does that help us along our way?

Answer 17

yes

Answer 18

What is the result after applying this information?

Answer 19

well it's vertical so i would use:(x)^2=4p(y-16)

Answer 20

Does that look familiar? 1/A = 4p

Answer 21

ohh yes the asymptote right?

Answer 22

No asymptote on a parabola. We don't have a Focus. We don't have a Directrix. How shall we find the value of p?

Answer 23

by moving the (y-16) to the other side?

Answer 24

No good. We need another value. Just substitute (8,0) into that equation with "p" and see what happens.

Answer 25

that's the focal width

Answer 26

i got p=1

Answer 27

Keep in mind that p < 0 because this is a downward opening parabola.

That MAY BE the focal width. Do we KNOW the Focus is at the Origin?

Answer 28

8^2=4p(0-16)

64 = 4*p*(-16) = -64p and we have p = -1

Answer 29

Okay, so what is the final equation?

Answer 30

(x)^2=-4(y-16)

Answer 31

And for our final act, what value of y corresponds to x = 1?

Answer 32

64=-4(y-16)

Answer 33

?? How does 1^2 = 64?

Answer 34

i thought it was the 64 from the top from 8^2

Answer 35

Why would you think that? The equation is x^2=-4(y-16)

Substitute x = 1.

Answer 36

because idk where that 1 came from
1=-4(y-16)

Answer 37

Solve for y.

Answer 38

can i distribute the -4?

Answer 39

If you want. Just find the value of y - any way you like.

Answer 40

i got y=16

Answer 41

Note: It had better be a little less than 16.

Answer 42

1=-4(y-16)

-1/4 = y-16

y = 16 - 1/4

Answer 43

i moved it all to the other side... i finally got 15.75

Answer 44

There it is. Can you now answer the question?

Answer 45

yes thank you for all of your help :)

Answer 46

Way to hang in there!! Understanding what the problem wanted was the first hard part. :-)

Answer 47

yes but you really clarified that :D