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?

Guest Jul 25, 2021

#1**+1 **

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

ElectricPavlov Jul 25, 2021