# Math, Trig

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A soccer player kicks a ball from the ground to a maximum height of 12 m. The high point in the trajectory of the ball occurs at a distance of 18 m from the kicker. On the downward path, another player heads the ball at a height of 2.2 m from the ground.

Write a quadratic function that models the situation.

my ans -
y = a (x+2.2)2 + 12
y = a (0 +2.2)2 + 12
12 = a(2.2)2
a = 12/(2.2)2
a= 2.47..

• Math, Trig -

y(0) = 0 and the vertex is at x=18 (halfway to the other root) and the parabola opens downward, so
y = ax(36-x)

the vertex is at (18,12) so

18a*(18) = 12
x = 12/18^2 = 2/3*18 = 2/54

y = 2/54 x(36-x)

• Math, Trig -

Thank you so much, Sir.

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