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Figure A shows a bridge across a river. The arch of the bridge is a parabola, and the six vertical cables that help support the road are equally spaced at $4-m$ intervals. Figure B shows the parabolic arch in an $x-y$ coordinate system, with the left end of the arch at the origin. As is indicated in Figure B, the length of the leftmost cable is $3.072 \ m$. Determine the equation in form $(x-h)^2 = -4p(y-k)$

Saket Gurjar
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air conditioner
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  • Where are the figures? – Vishu May 27 '20 at 19:39
  • Sorry, they're there now. – air conditioner May 27 '20 at 19:51
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    Note that the given parabola is of the form $y = ax(x - 28)$ since the roots are at $x = 0$ and $x = 28$ and $a < 0$. You can determine the value of $a$ using the fact that $(4, 3.072)$ is point on the parabola. Once you have determined the value, you can rearrange the equation in the required form. – sudeep5221 May 27 '20 at 19:55
  • I don’t see a question here. This is a bare problem statement, which makes it look like you’re trying to outsource your homework. If there’s something specific that you’re having trouble with, then show your work up until the point where you’re getting stuck and ask about that. See How to ask a homework question. – amd May 28 '20 at 02:33

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You know that $h=14$ from the figure and you're only missing p and k. You can easily pull three data points from the figure: (4, 3.072), (28,0), and (0,0). You can use two of those points with ${(x-14)}^2=-4p(y-k)$ to create a two equation, two variable system of equations and solve for p and k. I'll let you solve the rest.

Ty.
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  • I can't seem to get my system of equations correct. Currently, my equations are 100 = -4p(3.072 - k) and 196 = -4p(k). Each time I try to work through it I get the answer wrong. – air conditioner May 27 '20 at 20:29
  • The second equation should be 4pk not -4pk. – Ty. May 27 '20 at 20:33