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I have a very very simple quadratic function:

Now building a new tunnel that has a shape of parabolic curve. The tunnel is 10 m wide and at 4 m from either side, the height of the tunnel is 6 m. Find the quadratic equation in standard form that models the ceiling of the new tunnel.

The question is very simple, but I just can't understand what does at 4 m from either side mean in this question while mentioning the width in 10m?

I am not a native English speaker so it is hard for me understand what the information this question is asking.

Any comments and answers will be appreicated!

Edit: I see comments where people say that this question is badly word, I agree. Actually, this is a question I did on test and I just get the result today, none of the people in my class get the answer.

It not me made the question.

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  • $\begingroup$ At a point on the ground and 4 m from the side of the tunnel, the height of the tunnel measured from that point is 10 m. $\endgroup$
    – peterwhy
    Mar 23 at 0:50
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    $\begingroup$ Please pay attention to your tags when asking a question here. You're doing a good job at providing the right context to us so far: please keep it up! $\endgroup$
    – Toby Mak
    Mar 23 at 1:17
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    $\begingroup$ It's not just you; I (native English speaker) agree that the question is badly-worded. Its intent must be as both the current answers describe. But in real-life tunnels ‘width’ and ‘from side to side’ would usually refer to its cross-section (i.e. the point of view of someone travelling through the tunnel). The distance in the question would more usually be called ‘length’ — though that could also refer to distance travelled (i.e. arc length), which is not the same (even though it's in the same direction). $\endgroup$
    – gidds
    Mar 23 at 11:47
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    $\begingroup$ Indeed a very badly worded question. Not really clear what one should expect the "shape of a tunnel" to be, but I think most often it would refer to the trajectory when passing through the tunnel (which would for instance be level when passing through a mountain, but descending and then ascending when going underneath a river). However here it seems to refer to the shape of the arc formed by the tunnel ceiling at (maybe) the entrance. And it is very unrealistic: all tunnels I have ever seen have at least some portion of their lateral walls purely vertical, which is excluded by a parabola. $\endgroup$ Mar 23 at 12:39
  • $\begingroup$ @MarcvanLeeuwen, I totally agree. Actually, this is a question I did on test and I just get the result today, none of the people in my class get the correct answer. it not me made the question, my teacher did. $\endgroup$
    – Sahil
    Mar 23 at 22:13

2 Answers 2

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$\begingroup$

This figure would help you understand:

enter image description here

(To-scale figure,Credit :Dan) enter image description here

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    $\begingroup$ Did you deliberately sketch it with obviously wrong dimensions? $4 + (\approx 2\times 6) + 4 = 10$... $\endgroup$ Mar 23 at 11:52
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    $\begingroup$ @leftaroundabout it's a sketch to illustrate the problem, not an actual building plan. $\endgroup$ Mar 23 at 13:10
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    $\begingroup$ I made one that's actually a parabola, and to scale: i.stack.imgur.com/Cvht4.png $\endgroup$
    – Dan
    Mar 23 at 21:44
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    $\begingroup$ I prefer the previous obviously-not-to-scale diagram(!), because it has an implicit learning point: that a diagram can often serve its purpose without being scale-accurate and readers shouldn't assume that diagrams are to scale. $\endgroup$
    – ryang
    Mar 25 at 12:29
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$$f(0)=f(10)=0$$

$$f(4)=f(10-4)=6$$

The tunnel is 10 m wide and at 4 m from either side, the height of the tunnel is 6 m.

The sentence is split into two parts by the "and", not by the comma.

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