Problema Solution
The function f(x) = −0.002x2 + 0.66x models the path of a softball that is hit for a home run, where f(x) gives the height of the ball and x gives the distance from where it is hit in feet.
a. How far does the ball travel before hitting the ground?
b. How high does the ball go?
c. What is a reasonable domain and range for a home run modeling function?
Answer provided by our tutors
a. How far does the ball travel before hitting the ground?
We need to find positive x such that f(x) = 0 (when the ball hits the ground the height equals to 0)
−0.002x^2 + 0.66x = 0
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click here to see the equation solved for x
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x = 330 ft
The ball will travel a distance of 330 ft.
b. How high does the ball go?
To find the maximum height we need to find the vertex of the parabolic function: f(x) = −0.002x^2 + 0.66x
f max = c - b^2/4a, where a = -0.002, b = 0.66, c = 0
f max = - 0.66^2/(4*(-0.002))
f max = 54.45 ft
The ball will go 54.45 ft high.
c. What is a reasonable domain and range for a home run modeling function?
For the function f(x) = −0.002x^2 + 0.66x:
the domain is: (0, 330)
the range: (0, 54.45)