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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1.1 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -4.88088481701516, 204.880884817015. Here's your graph:

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

Answer by ewatrrr(24785) (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? 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 .

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