SOLUTION: Hi, I could really use some help with this. I think I can figure it out if I could just get the quadratic function right, so any help would be appreciated. A horizontal bridge

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Question 76195This question is from textbook College Algebra Essentials
: Hi, I could really use some help with this. I think I can figure it out if I could just get the quadratic function right, so any help would be appreciated.
A horizontal bridge is in the shape of a parabolic arch. Given the information shown in the figure (base is 20 ft, height in middle is 10 ft), what is the height h of the arch 2 feet from shore?
Thank you,
JodiThis question is from textbook College Algebra Essentials

Answer by scott8148(5891) About Me  (Show Source):
You can put this solution on YOUR website!
if you picture the bridge sitting on the x-axis and centered on the y-axis, then the parabola passes through (-10,0), (0,10), and (10,0)

the parabola has the form y=ax%5E2%2Bbx%2Bc

substituting (0,10) gives c=10

substituting (-10,0) gives 0=100a-10b+10

substituting (10,0) gives 0=100a+10b+10...adding the previous equation gives 0=200a+20...or a=-.1...so b=0

the equation for the parabola is y=-.1x%5E2%2B10...so for x=8(or -8), y=3.6

you can locate the parabola anywhere and it will change the values of constants, but the answer will be the same