Quadratics investigation

[Jade727]

Hi, I was given a quadratics investigation at school and was wondering if someone could offer any help!

The Sydney Harbour Bridge roadway is 504m long. At a distance of 108.5m from each pylon, there is a vertical strut extending from the lower arch to the roadway (as shown in the image). Here the lower arch is 80m above sea level and the upper arch is 49m above the roadway. 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 form
- intercept form
- general form

 

[Deleted member 4993]

Hi, I was given a quadratics investigation at school and was wondering if someone could offer any help!

The Sydney Harbour Bridge roadway is 504m long. At a distance of 108.5m from each pylon, there is a vertical strut extending from the lower arch to the roadway (as shown in the image). Here the lower arch is 80m above sea level and the upper arch is 49m above the roadway. 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 form
- intercept form
- general form

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.

The problem says - "as shown in the image". Where is the image?

 

[Jade727]

Sorry about that, I will attach the image and my working out now. I do not believe that I have used the information correctly, and I cannot figure out how to solve the question using the information. If you can offer any sort of help I would greatly appreciate it!

 

[Dr.Peterson]

(a) Why did you set h = 80? and why is x replaced by 0 on the right but not on the left?

(b) Why did you replace x with different numbers in different places?

(c) The definition of f(x) ought to have an x in it, shouldn't it?

Before you write equations, you should explicitly state where your coordinate system is, and what points are the vertex, intercepts, etc.

Give it another try, and write out the reasons for each thing you do in words. Believe it or not, words are allowed in math, and actually help you think!

I'd start by sketching the parabola on a coordinate plane and labeling all the points described in the problem.

 

[Steven G]

I have to ask just what Dr Peterson asked in his post. Why did you replace x with different values? x is unknown, but that does not mean it can equal different values throughout an equation. One equation gets one and only one x-value.

 

[Dr.Peterson]

The Sydney Harbour Bridge roadway is 504m long. At a distance of 108.5m from each pylon, there is a vertical strut extending from the lower arch to the roadway (as shown in the image). Here the lower arch is 80m above sea level and the upper arch is 49m above the roadway. At the vertices, the lower arch is 118m above sea level and the upper arch is 73m above the roadway.

I'll start you off:

I'll take your idea of x=0 at one pylon and x=504 at the other (assuming that's the meaning of the length of the roadway), and y=0 for sealevel. Then the point (108.5, 80) is on the lower arch. The vertex will be halfway along the bridge, so x = 252 and y = 118. (I think we're ignoring the upper arch and the roadway height.)

Now, find the equation in any form; don't think that the vertex, intercept, and general forms all have to be found in that order, or one at a time. You may find that the vertex form gives you values for everything but a, and another form can give you a, for example.

You'll also find that there is too much information; the last point can be used to check that the arch really is close to parabolic.

 

[Jade727]

Thank you very much for your replies, they have been extremely helpful. I used the x and y coordinates that you suggested and found myself figuring out the answers so thank you, I really appreciate it