Sydney Harbour Quadratics

[zavierl]

Hi! I would first like to greatly appreciate anyone who is willing to help with my problem. I also wasn't too sure where to post this as there was no designated quadratics forum. I have this question:
"The Sydney Harbour Bridge roadway is 504m long. There are vertical struts extending from the lower arch to the roadway (as shown in image). At the vertices, the lower arch is 118m above sea level and the upper arch is 73m above the roadway. Find the quadratic equations which describe the parabolas of the lower arch in vertex, intercept and general form."

I know to begin on vertex form, your h and k values are the x and y of the vertex. I have made the vertex of the lower arch (252, 118). This is because halfway of 504 is 252 and the 118m is given. Is this correct?

I am also stuck on where to go from there as I do not know any other value I could use. I have my x axis at sea level, however, would it be better to have my x axis at road level so I can use some x intercept points?

Any help would be greatly appreciated. Thank you!

 

[lev888]

Why is the lower arch higher than the upper?

 

[Dr.Peterson]

"The Sydney Harbour Bridge roadway is 504m long. There are vertical struts extending from the lower arch to the roadway (as shown in image). At the vertices, the lower arch is 118m above sea level and the upper arch is 73m above the roadway. Find the quadratic equations which describe the parabolas of the lower arch in vertex, intercept and general form."

Is this all the information you have? Since the vertices are described with respect to different bases (sea level vs the roadway), we need to know how high the road is (if you were asked about the upper arch, which I see we aren't, yet). Are you expected to estimate by measuring on the picture?

I know to begin on vertex form, your h and k values are the x and y of the vertex. I have made the vertex of the lower arch (252, 118). This is because halfway of 504 is 252 and the 118m is given. Is this correct?

Yes.

I am also stuck on where to go from there as I do not know any other value I could use. I have my x axis at sea level, however, would it be better to have my x axis at road level so I can use some x intercept points?

You could use either as the x-axis. I'd probably use sea level, because then the x-intercepts are known. (I'm taking the length as the distance between those intercepts.)

 

[zavierl]

Why is the lower arch higher than the upper?

I don’t think it is. The lower arch’s position is stated in respect to the sea level, while the upper arch is in respect to the roadway, which is higher than the sea level

 

[zavierl]

Is this all the information you have? Since the vertices are described with respect to different bases (sea level vs the roadway), we need to know how high the road is (if you were asked about the upper arch, which I see we aren't, yet). Are you expected to estimate by measuring on the picture?


Yes.


You could use either as the x-axis. I'd probably use sea level, because then the x-intercepts are known. (I'm taking the length as the distance between those intercepts.)

If the sea level is my x axis, what would the intercepts be? Because wouldn’t the left side (hopefully) stop at (0,0) but not pass through the x axis as it can’t go below sea level?

 

[zavierl]

If the sea level is my x axis, what would the intercepts be? Because wouldn’t the left side (hopefully) stop at (0,0) but not pass through the x axis as it can’t go below sea level?

This is also all the information we have which is why I was getting stuck. I thought we would be told a distance from a pillar to a strut but not ?‍. I’d say we aren’t expected to measure because part b is to find the difference in higher from the lower arch to the higher arch which is where I believe finding the distance from sea level to road level would be important, but I decided to first solve part a, haha ?

 

[lev888]

I don’t think it is. The lower arch’s position is stated in respect to the sea level, while the upper arch is in respect to the roadway, which is higher than the sea level

Thanks, didn't notice the difference.

 

[Dr.Peterson]

If the sea level is my x axis, what would the intercepts be? Because wouldn’t the left side (hopefully) stop at (0,0) but not pass through the x axis as it can’t go below sea level?

"The Sydney Harbour Bridge roadway is 504m long. There are vertical struts extending from the lower arch to the roadway (as shown in image). At the vertices, the lower arch is 118m above sea level and the upper arch is 73m above the roadway. Find the quadratic equations which describe the parabolas of the lower arch in vertex, intercept and general form."

We have to decide how to interpret some details; in particular, as I said before,

(I'm taking the length as the distance between those intercepts.)

That is, the (near side of the) pylons more or less mark the intercepts with sea level, so we can take the roadway as extending between those.

If you're thinking the curve has to actually pass through an intercept, that's not true (though it will be true for the parabola you are using to model the arch). Just think of the intercept as where it reaches the x-axis.

So I'm taking it like this:



Does that make sense? What are the intercepts now? Where is the vertex?

This is also all the information we have which is why I was getting stuck. I thought we would be told a distance from a pillar to a strut but not ?‍. I’d say we aren’t expected to measure because part b is to find the difference in higher from the lower arch to the higher arch which is where I believe finding the distance from sea level to road level would be important, but I decided to first solve part a, haha ?

If by "pillar" you mean "pylon", I don't see how the distance from that to each of the 30 or so struts is needed; but we do need some additional vertical information. Perhaps you can show us the entire problem (which we ask for in general, to make sure nothing is missing), and we can see what you have to use.