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You throw a ball toward a trash can. The ball follows a parabolic path through (10, 10), (−14, 10), and (20, 7). What is the equation of the parabolic path?

 Jul 25, 2021
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the points (10, 10), (−14, 10)  show the axis of symmetry to be   -2    ( midway between 10 and -14)

  so the x coordinate of the vertex is -2         vertex = (-2,k)

 

Vertex form of the parabola

y = a (x+2)^2  +k     sub in the first point in the list

10 = a (12)^2 + k

10 = 144a + k

 

Sub in another point ( I'll use the third one)

7 = a (22)^2 +k

7 = 484a + k               Two equations with two unknowns <====== solve to find a = -3/340        k =   11 23/85

 

Your parabola becomes

y = -3/340 ( x+2)^2   + 11  23/85

 

 

Here is a confimational graph:

https://www.desmos.com/calculator/k2brpujphy

 Jul 25, 2021

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