Quadratic Functions, Confusion, and Algebra...OH MYYYY

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Hi I'm in urgent need of help. I'm completely confused on how to solve this problem. If you could tell me how to solve the problem in simplish INCREDIBLY DETAILED terms so I can work out the problem by myself and understand the material as best as possible, or just show me how you got the answer. I really just need the quadratic function answer and hints on how to solve the rest. Thanks so much in advance!!!

A new device created by the local pet shop allows the owner to stomp on a lever to send the ball flying through the air. This device has become so popular that the council wants to install a few of them in a specialized area. It is suggested that a rectangular plot of land be set aside for this Activity. The lot will be 27 feet wide and 35 feet long. A fence needs to surround the perimeter of this lot so that people will not lose their ball when it is thrown.
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The city council needs to know what would be a reasonable height for the fence, which goes around the perimeter of the lot, so people, on average, will not lose their balls when playing fetch with their pets.

Here we investigate the path of a ball thrown by different people.

Various persons were asked to stomp on the device and send a ball flying. The following averages were obtained
Person Average Distance Traveled Max. Height
17 year old 49 feet 16 feet
45-year-old 38 feet 12 feet

Determine a quadratic function for each person for the height of the ball (in feet) in terms of the horizontal distance.
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Complete the following table to show at what height each ball will hit the fence. Since the field will be 35 feet long, the position of the fence would be indicated by x = 35 (side note ????????=blanks)
x y1=??????? y2=????????
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I'm guessing x would be 35 in each of the x blanks?

 

[mmm4444bot]

Determine a quadratic function … for the height of the ball (in feet) in terms of the horizontal distance [x].

or just show me how you got the answer I will show an example.

Example: the ball lands 50 feet from where it starts, and it reaches a height of 20 feet.

The variable x represents the horizontal distance away from the starting point.

The variable y represents the height of the ball.

:idea: Since the ball sails along a parabolic path, the highest point is at the vertex. :idea:

The vertex occurs halfway between the starting point and the landing point, so the vertex coordinates are (25, 20).

Two other points for which we know the coordinates are the starting point (0, 0) and the landing point (50, 0)

:idea: The equation for a parabolic graph is: y = Ax^2 + Bx + C :idea:

where A, B, and C represent values that you need to find.

:idea: Substituting the (x, y) coordinates from the three points gives a system of three equations. :idea:

(0, 0) leads to the equation C = 0.

(50, 0) and C = 0 give the equation: 2500A + 50B = 0

(25, 20) and C = 0 give: 625A + 25B = 20

Solving these last two equations shows that A = -4/125 and B = 8/5.

Therefore, the function for the height of the ball (y) in terms of the horizontal distance that it travels (x) is:

y = -(4/125)x^2 + (8/5)x

From this we find that y = 84/5 when x = 35

That is, the ball is 16.8 feet above the fence line.

Can you form specific questions about what you don't understand ?