Question

A bottle rocket travels along a parabolic path and reaches a maximum height of 21 feet after traveling a horizontal distance of 7 feet.

A) Write a quadratic function of the form y=a(x-h)^2 +k that models the bottle rocket's path, assuming it leaves the ground at the point (0,0).

B) Describe how changing the values of a, h, and k affect the flight path of the bottle rocket.

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for A) a classmate got y=-3/7 (x-7)^2 +21 ... I was wondering how they got that as their answer ... Oh wait so they divided 7 by 21 to get the 3 ?

Answer 1

the vertex of your parabolic path is (7,21)

so y = a(x-7)^2 + 21
but (0,0) lies on it, so
0 = a(0-7)^2 + 21
0 = 49a + 21
49a = -21
a = -21/49 = -3/7

so y = (-3/7)(x - 7)^2 + 21