SOLUTION: PLEASE HELP!! The height of a ball is modeled by the equation y=-1/70 x^2+2x+2 where x is the horizontal feet and y the vertical feet. A) How high is the ball when you hit

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Question 301224: PLEASE HELP!!
The height of a ball is modeled by the equation y=-1/70 x^2+2x+2 where x is the horizontal feet and y the vertical feet.
A) How high is the ball when you hit it?
B) What is the ball's maximum heigh?
C) How far from where you hit the ball does it strike the ground?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The height of a ball is modeled by the equation y=-1/70 x^2+2x+2 where x is the horizontal feet and y the vertical feet.
A) How high is the ball when you hit it?
Assuming x is the distance from where it's hit:
x = 0 --> y = 2
-----------------
B) What is the ball's maximum heigh?
It's a parabola, find the vertex:
@ x = -b/2a = -2/(-1/35) = 70
y = -(1/70)*70^2 + 140 + 2
y = 72
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C) How far from where you hit the ball does it strike the ground?
At y = 0
-x^2/70 + 2x + 2 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -0.0142857142857143x%5E2%2B2x%2B2+=+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=%282%29%5E2-4%2A-0.0142857142857143%2A2=4.11428571428571.

Discriminant d=4.11428571428571 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+4.11428571428571+%29%29%2F2%5Ca.




Quadratic expression -0.0142857142857143x%5E2%2B2x%2B2 can be factored:
-0.0142857142857143x%5E2%2B2x%2B2+=+%28x--0.992957397195394%29%2A%28x-140.992957397195%29
Again, the answer is: -0.992957397195394, 140.992957397195. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-0.0142857142857143%2Ax%5E2%2B2%2Ax%2B2+%29


=~ 140.993 feet