SOLUTION: The path traveled by a ball hit into the air can be modeled with the quadratic function, y = -0.042x^+5x, where x is the distance in yards from the point it was hit and y is the he

Question 448887: The path traveled by a ball hit into the air can be modeled with the quadratic function, y = -0.042x^+5x, where x is the distance in yards from the point it was hit and y is the height the ball reached in feet. Assuming that the ground is level.
a) Find the maximum height reached by the ball.
b) How far from where it was hit does the ball hit the ground?
Please help me with this problem as I am getting a negative figure for the height. There is something I am not doing correct.
Thank you. I look forward for your assistance with this problem.
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
y = -0.042x^2+5x [you left out the 2]
a) The maximum height reached will be the height at which dy/dx = 0
dy/dx = 0 = (2)(-0.042)x + 5
Solve for x:
0 = -0.084x + 5
x = 59.52 ft. along the ground.
Therefore, the maximum height is:
y = -0.042*(59.52)^2 + 5*59.52 = 148.81 ft.
b) We need to set y=0 and solve for x:
0 = -0.042x^2 + 5x
0 = x(-0.042x + 5)
This gives x = 0 [the starting point]
and x = -5/-0.042 = 119.05 ft.
The graph is below:

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