SOLUTION: Hello, may I please get some assistance on determining the variables to this algebra word problem. The problem is in reference to an arch. It states to use f(x)=a(x-h)2 +k

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Question 911710: Hello, may I please get some assistance on determining the variables to this algebra word problem. The problem is in reference to an arch. It states to use
f(x)=a(x-h)2 +k
The arch is 290 feet high
The arch is 275 feet wide at ground level.
The function you find should assume that the arch is placed in a coordinate system in which the x axis is at ground level and the y axis goes through the left hand side at ground level. Basically I need to know where on the arch to position a rope that would reach the bottom of the arch. The word problem references this as a bungee jumping scenerio which is why they are asking for the positioning of the rope on the arch. I am to assume a rope length of 272 feet long. So where on the arch would I place the 272 foot long rope and have it touch the ground level of the arch? I am to use f(x)=a(x-h)2 +k to determine the solution. Thank you!




Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Your bungee chord description is confusing. The equation for the arch can be formed.

The arch is based on y=ax%5E2 and a%3C0. The vertex has been moved to x=275%2F2 and y=290.


f%28x%29=a%28x-275%2F2%29%5E2%2B290, and one of the x-intercepts is (0,275).


a%28x-275%2F2%29%5E2%2B290=f%28x%29

a%28x-275%2F2%29%5E2=f%28x%29-290

a=%28f%28x%29-290%29%2F%28x-275%2F2%29%5E2

Substitute the point
a=%28275-290%29%2F%28275-275%2F2%29%5E2

a=%28-15%29%2F%2818906%261%2F4%29

a=-%2860%2F75625%29

highlight_green%28a=-12%2F15125%29

Using integers as much as possible,
highlight%28f%28x%29=-%2812%2F15125%29%28x-275%2F2%29%5E2%2B290%29, for the arch.