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# 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.

### 1 Answer

- davidLv 71 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