Question 1760: I need to come up with the general equation of a quadratic function for the following word problem. Can you help me get started please?
A large awning is being designed for a hotel entrance and drive. The roof is to be a section of a parabola, with the vertex attached to the hotel wall 16 feet abve the ground, and supported by 10 foot wall posts that are 12 feet away from the hotel wall.
Come up with a general eqaution of a quadratic function that would model the roof of the awning.
Thanks for ANY help. I'm completely stuck on how to go about this problem algebraically.
Noelle
marknoni@comcast.net
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! to start with this...draw a picture. Draw a vertical line for the wall and a floor line. Draw a rough curve from the wall arcing down and mark on the height 16 feet, the pole, 10 feet and te distance from the wall, 12 feet.
The leap of faith you need is to visualise this as a graph. Extend the wall up and call this the y-axis. Where the awning touches the wall, draw a horizontal line for the x-axis. Now carry on the awning curve to the other lower quadrant of your graph, so you have a classic parabola shape.
What you know is the following:
1. the curve passes through the origin of these axes (0,0).
2. the curve passes through 2 other points that we know...namely (12, -6) and (-12,6). Have a think about these and see if you can see where these numbers come from. They are the points where the awning touches the top of the pole.
Now, we just have to fit this 2 bits of info to the general equation of a parabola...  .
To do this, we put the info we know into the general equation...First, we know that x=0 when y=0. This gives us that c must be zero. Therefore our equation is now of the form  .
I shall leave you to do the rest :-)
Note, the curve is an "upside down parabola" so you should get a to be a negative number.
Jon
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