A shot-putter throws a ball at an inclination of 45° to the horizontal. The following data represent the height of the ball h at the instant that it has traveled x feet horizontally.

Distance, x ………………………. Height, h

20 …………………………………..……. 25

40 …………………………………..……. 40

60 …………………………………..….…. 55

80 …………………………………..….…. 65

100 …………………………………..……. 71

120 …………………………………..……. 77

140 …………………………………..……. 77

160 …………………………………..……. 75

180 …………………………………..……. 71

200 …………………………………..……. 64

(a) Use a graphing utility to draw a scatter diagram of the data. Comment on the type of relation that may exist between the two variables.

(b) Use a graphing utility to find the quadratic function of best fit that models the relation between distance and height.

(c) Use the function found in part (b) to determine how far the ball will travel before it reaches its maximum height.

(d) Use the function found in part (b) to find the maximum height of the ball.

(e) With a graphing utility, graph the quadratic function of best fit on the scatter diagram.