Question 802814: An engineer is designing a parabolic arch. The arch must be 15m high and 6m wide at a height of 8m. Determine a quadratic function that satisfies these conditions and the width of the arch at its base.
This is what I have so far:
vertex (x,15)
passes through point (6,8)
h(w)= a(x-h)^2+15
Can you help me with the rest.
Thanks
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If it passes through point (6,8), it would need to pass through (0,8); the vertex will be at (3,15), and the base will be from a point (-b,0), to a point (6+b,0).
That makes it complicated.
Let's put the origin (0,0) at a point on the ground, directly below the vertex.
We make the line that passes through the feet of the arch the x-axis.
We call the vertical axis of symmetry of the arch our y-axis.
We measure x (the horizontal distance to the origin) in meters,
and y or h(x) (the height above the ground) also in meters.
 is our equation
The vertex will be (0,15).
The points at a height of 8 meters will be (-3,8) and (3,8), so that the arch width at that height is the (horizontal distance from (-3,8) to 3,8, which is 6.
Substituting the coordinates of (3,8), we get
At the base,  and
 needs to be solved
The feet of the arch are at  and 
and the width at the base is
 = approx. 7.75 meters
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