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?
+36916 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
