SOLUTION: The path of tennis ball during a serve is given by h(x)=0.002x^2-0.03x+8, where h(x) is the height of the ball in feet x feet from the server. For a serve to be legal in tennis, th

Question 1119183: The path of tennis ball during a serve is given by h(x)=0.002x^2-0.03x+8, where h(x) is the height of the ball in feet x feet from the server. For a serve to be legal in tennis, the ball must be at least 3 feet high when it is 39 feet from the server, and it must land in a spot that is less than 60 feet from the server. Does the path of the ball satisfy the conditions of a legal serve?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i believe your formula is incorrect.

you have:

h(x) = .002x^2 - 0.03x + 8

this results in a curve that bottoms out in the middle and extends upward on into infinity, never touching the ground.

that curve looks like this:

$$$

i believe you should have:

h(x) = -.002x^2 - 0.03x + 8

that curve looks like this:

$$$

given what i believe your equation should be, then:

the ball is at least 3 feet high 39 feet from the server and the ball touches the ground less than 60 feet from the server.

it therefore satisfies the conditions for a legal serve.

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