Baby asked in Science & MathematicsMathematics · 1 month ago

# A soccer player kicks a ball?

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.

a. Write a quadratic function that models the situation.

b. How far from the kicker in the line of the trajectory must a player be to head the

ball as described? Give the answer to two decimal places.

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• david
Lv 7
1 month ago

x = distance from kicker

y = height of ball

(0,0)  <<<  original place where ball is kicked

(18, 12)  <<<  hghest point

because of symmetry  (36,0) should be another point .. except for the header

y = ax^2 + bx + c

0 = a(0) + b(0) + c  ..  c = 0

12 = a(18^2) + b(18)

0 = a(36^2) + b(36)  ...  b= -36a

12 = 324a + 18b

12 = 324a + 18(-36a)  ...  a = -12/324 = -1/27

b = +4/3

. . . y = -(1/27)x^2  + (4/3)x  <<<  quadratic

y = 2.2 .. x = ? . .

2.2 = -(1/27)x^2 + (4/3)x  <<<  solve for x

x = 34.2665 m

y = -(1/27)x^2 + (4/3)x   for   0 < x < 34.2665

the quadratic must have a limited domain  because of the header