Question

You are playing tennis with a friend.The path of the tennis ball after you return to a serve can be modeled by the function y=-0.005x^2 + 0.17x + 3, where X is the horizontal distance (in feet) from where you hit the ball and Y is the height (in feet) of the ball. Question 1. (what is the maximum height of the tennis ball) Question 2. (You are standing 30 feet from the net, which is 3 feet high.Will the ball clear the net? Explain your reason.)

Answer 1

#1) 4.445 ft
#2) yes

Step-by-step explanation
#1) The maximum height is the y-coordinate of the vertex. We first find the axis of symmetry, given by x=-b/2a:

x=-0.17/2(-0.005) = -0.17/-0.01 = 17

Plugging this into the equation,
y=-0.005(17²)+0.17(17)+3 = 4.445

#2) Substituting 30 into the equation,
y=-0.005(30²) + 0.17(30) + 3 = 3.6

The ball will 3.6 in the air, so yes, it will clear the 3 ft tall net.