SOLUTION: a ball is thrown across a playing field. it’s path is by the equation y=-0.005x^2 +x+5 where x is the distance the ball has traveled horizontally. and y is it’s height above gr

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Question 1197419: a ball is thrown across a playing field. it’s path is by the equation y=-0.005x^2 +x+5 where x is the distance the ball has traveled horizontally. and y is it’s height above ground level, both measured in feet. what is the maximum height attained by the ball? how far has it traveled horizontally when it hits the ground
Found 2 solutions by Alan3354, ewatrrr:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a ball is thrown across a playing field. it’s [sic] path is by the equation y=-0.005x^2 +x+5 where x is the distance the ball has traveled horizontally. and y is it’s [sic] height above ground level, both measured in feet. what is the maximum height attained by the ball? how far has it traveled horizontally when it hits the ground
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it's = it is
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y=-0.005x^2 +x+5 is a parabola
The vertex is at x = -b/2a = -1/-0.01 = 100
Sub 100 for x:
y = -0.005*10000 + 100 + 5 = 155 feet, the max height
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y=-0.005x^2 +x+5
Find x when y = zero
-0.005x^2 +x+5 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.005x%5E2%2B1x%2B5+=+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=%281%29%5E2-4%2A-0.005%2A5=1.1.

Discriminant d=1.1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+1.1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+1.1+%29%29%2F2%5C-0.005+=+-4.88088481701516
x%5B2%5D+=+%28-%281%29-sqrt%28+1.1+%29%29%2F2%5C-0.005+=+204.880884817015

Quadratic expression -0.005x%5E2%2B1x%2B5 can be factored:
-0.005x%5E2%2B1x%2B5+=+%28x--4.88088481701516%29%2A%28x-204.880884817015%29
Again, the answer is: -4.88088481701516, 204.880884817015. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.005%2Ax%5E2%2B1%2Ax%2B5+%29

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Ignore the negative value, and, no it CANNOT be factored.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


y=-0.005x^2 +x+5  (max at x = 100) y' = 0 ⇒ -.01x + 1 = 0 , x = 100
maximum P(100,55)
what is the maximum height attained by the ball? 55ft
Can see from graph travels 'approximately' from -5 to 205 0r  ~210ft 

Recommend using a Graphing software as a visual aid and calculator
FREE graphing software is available at http://www.padowan.dk.com

Below a screenshot of y=-0.005x^2 +x+5  using that software:
Using its 'evaluate' feature can also give a closer approximation to x-intercepts
 .