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# The distance from the edge of the centre circle toward the goal and y is the height of the ball.?

A soccer player kicks the ball from a position 17.5 m in front of the goal line. The quadratic function y=-0.05(x-20)(x-40) describes the path of the ball, where x is the distance from the edge of the centre circle toward the goal and y is the height of the ball.

a. What are the coordinates of the points where the ball theoretically touches the ground?

b. What is the maximum height of the ball during its flight

### 1 Answer

- AshLv 71 month agoFavorite Answer
y=-0.05(x-20)(x-40) .....(1)

When the ball touches the ground, y = 0

So we need to find x, when y = 0

Now plug in (1)

0=-0.05(x-20)(x-40)

0 = (x-20)(x-40)

x = 20 and x = 40

The ball touches the ball at 40 m from the edge of the centre circle

b. At max height vertical velocity = 0

vertical velocity = y'

y' = -0.05[(x-40) + (x-20)]

0 = -0.05(2x-60)

2x-60 = 0

2x = 60

x = 30

At x=15, find y

y = -0.05(30-20)(30-40) = 5 m

Max height of the ball = 5 m