SOLUTION: height y (in feet) of punted football is approximated by y = -16/2025 x^2 +9/5x + 5/2 where x is horizontal distance (in feet ) from point at which the ball is punted . (a)use a

Algebra ->  Graphs -> SOLUTION: height y (in feet) of punted football is approximated by y = -16/2025 x^2 +9/5x + 5/2 where x is horizontal distance (in feet ) from point at which the ball is punted . (a)use a      Log On


   



Question 1058616: height y (in feet) of punted football is approximated by y = -16/2025 x^2 +9/5x + 5/2 where x is horizontal distance (in feet ) from point at which the ball is punted .
(a)use a graphing utility to graph the path of football.
(b)how high is the ball when it is punted ?(find y when x=0)
(c)what is the maximum height of football?(round your answer to two decimal places)
(d)how far from punter does the football strike the ground?(round your answer to two decimal places)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
height y (in feet) of punted football is approximated by y = -16/2025 x^2 +9/5x + 5/2 where x is horizontal distance (in feet ) from point at which the ball is punted.
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(a)use a graphing utility to graph the path of football.
dl the FREE graph software at www.padowan.dk
Use Insert, enter -16x^2/2025 + 9x/5 + 5/2
Pick a color
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(b)how high is the ball when it is punted ?(find y when x=0)
2.5 feet
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(c)what is the maximum height of football?(round your answer to two decimal places)
It's the vertex of the parabola at x = -b/2a
x = (-9/5)/(-32/2025) = 9*2025/150 = 121.5
y = 31.66 feet
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(d)how far from punter does the football strike the ground?(round your answer to two decimal places)
Find x when y = 0
y = -16/2025 x^2 +9/5x + 5/2 = 0
16x^2 - 3645x - 5062.5 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B-3645x%2B-5062.5+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3645%29%5E2-4%2A16%2A-5062.5=13610025.

Discriminant d=13610025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3645%2B-sqrt%28+13610025+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3645%29%2Bsqrt%28+13610025+%29%29%2F2%5C16+=+229.19302304471
x%5B2%5D+=+%28-%28-3645%29-sqrt%28+13610025+%29%29%2F2%5C16+=+-1.38052304471012

Quadratic expression 16x%5E2%2B-3645x%2B-5062.5 can be factored:
16x%5E2%2B-3645x%2B-5062.5+=+%28x-229.19302304471%29%2A%28x--1.38052304471012%29
Again, the answer is: 229.19302304471, -1.38052304471012. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-3645%2Ax%2B-5062.5+%29

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Ignore the negative value
x =~ 229.19 feet