SOLUTION: Aunt Barbara has a doorway in the shape of a parabola. Find an equation describing the door given that is 4 feet across and 8 feet high in the center. Determine the width of the do
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Question 1169046: Aunt Barbara has a doorway in the shape of a parabola. Find an equation describing the door given that is 4 feet across and 8 feet high in the center. Determine the width of the doorway at a point 5 feet off the ground.
Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!
Presuming that the door is 4 feet across at the bottom (something that the question didn't make clear and should have -- Please complain to your instructor about questions that want you to make unwarranted assumptions.) this can be modeled by a quadratic equation with a negative lead coefficient so that the parabola opens downward. To keep the function as simple as possible, eliminate the constant and first degree terms by placing the vertex at the origin. That gives us 3 points on our parabola: )
, )
, and )
. (Note that it is a horizontal distance of 4 between and .)
Since a parabola is modeled by a quadratic function, we can begin with
\ =\ ax^2\ +\ bx\ +\ c)
Since is on the graph:
\ +\ b(0)\ +\ c\ =\ 0)
So, as suggested earlier, 
Then since )
and are on the graph:
and
So 
and 
And that makes the function
\ =\ -2x^2)
The width at 5 feet above the floor has to be the width of the function at -3 which is 5 above -8
^2\ =\ -3)
I'll let you solve for 
John
My calculator said it, I believe it, that settles it
From
I > Ø
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