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When coming back from lunch, I bet Alayna that I could kick a beach ball across the Junior lot and hit Spencer's car. To hit his car I needed to kick the ball at a maximum of 30 feet. If i'm standing in the corner of the Junior lot and Spencer's car is 20 feet away, do I hit it?

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Uploaded by natalieantoinettee on 2016-12-08.

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-1
[0      0   1]     [ 3]       [a]
[144 12  1] •  [33] =  [b]
[576 -24 1]    [ 0 ]      [c]

After plugging in x, x^2 and y, we multiplied the inverse of Matrix A times Matrix B to find A, B and C

[a]         [ -.066]
[b]  =    [1.708 ]
[c]        [     3     ]

these values give you the equation:

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Y= -.066x^2+1.708x+3

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We used the quadratic formula to find the solutions of our equation. The solutions were (-1.652, 0) and (27.53, 0). These points represent where the ball was initially kicked and where the ball hit the ground.

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Y=-.066x^2+1.708x+3
Y=-.066(0)^2+1.708(0)+3
Y=0+0+3
Y=3
(0,3)

The y-intercept represents the point that my foot touched the ball for the initial kick, the ball was 3 feet off the ground when I kicked it.

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The Vertex is, (12, 33). It is the max height the ball reaches after kicking it and it is also halfway between where I initially kicked the all and where the ball landed.
If the ball went 33 feet in the air and 24 feet horizontally, your vertex would be the halfway point horizontally 24/2 = 12 and the highest point vertically which was 33 giving you the point (12,33)