# System of Equations

After a football is kicked, it reaches a maximum height of 14 m and it hits the ground 32m from where it was kicked. After a soccer ball is kicked, it reaches a maximum height of 8m and it hits the ground 38m from where it was kicked. The paths of both balls are parabolas.

a) create an equation that represents the path of the football.
b) To the nearest tenth of a metre, determine the horizontal distance that both balls have travelled when they are at the same height.

1. football for example:
starts at (0,0)
vertex at (16, 14) {get it ?}
ground again at (
(32,0)

a (y - 14) = (x-16)^2 or something maybe?
what is a?
goes through (0,0)
so
-14 a = 16^2 = 256
a = -18.3 approx

so
-18.3 (y-14) = (x-16)^2 = x^2 - 32 x + 256 = -18.3 y + 256
or
-18.3 y = x^2 - 32 x

posted by Damon

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