Parabolic Arch word problem

A

asheppard13

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An arch is 10 feet wide at its base. At a distance of 1 base foot, the arch has a height of 3.6 feet.
A. Sketch a graph of this scenario if the left end is the origin.
B. Find the equation in factored form which models the arch.
C. Convert the equation in part b to general form.
D. Find the maximum height of the arch and its horizontal distance from the left end to that height.
 
asheppard13 said:
An arch is 10 feet wide at its base. At a distance of 1 base foot, the arch has a height of 3.6 feet.
A. Sketch a graph of this scenario if the left end is the origin.
B. Find the equation in factored form which models the arch.
C. Convert the equation in part b to general form.
D. Find the maximum height of the arch and its horizontal distance from the left end to that height.
Click to expand...
What is the equation of a parabola, with vertex at (5,h)?

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

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Please share your work/thoughts about this problem
 
LCKurtz said:
Hint: A parabola that passes through [MATH](0,0)[/MATH] and [MATH](10,0)[/MATH] must have the form [MATH]y=ax(x-10)[/MATH].
Click to expand...
And the fact that "At a distance of one base foot" (which I take to mean one foot in from the base so either x= 1 or x= 9) "the arch has a height of 3.6 feet" tells us that 3.6= a(1)(1- 10)= =-9a and 3.6= a(9)(9- 10)= -9a. Solve that for a.
 
I realise the title of the post includes the word "parabolic", but the question itself doesn't. What if the arch had vertical sides with a semicircle on top? That would make a good question too!!
 
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