SOLUTION: Jake Johnson dives off the high dive at a pool. His distance from the surface of the water varies quadratically with the number of seconds that have passed since he left the board.

Question 147844: Jake Johnson dives off the high dive at a pool. His distance from the surface of the water varies quadratically with the number of seconds that have passed since he left the board. His distances at times of 1, 2, and 3 seconds since he left the board are 24, 18, and 2 meters above the water, respectively.
How do you write the particular equation expressing distance in terms of time?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Jake Johnson dives off the high dive at a pool. His distance from the surface of the water varies quadratically with the number of seconds that have passed since he left the board. His distances at times of 1, 2, and 3 seconds since he left the board are 24, 18, and 2 meters above the water, respectively.
How do you write the particular equation expressing distance in terms of time?
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You have three points: (1,24), (2,18), (3,2)
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Form of the equation: y = ax^2 + bx + c
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Substitute each of the ordered pairs into the form to get three
equations with variables a, b, and c.
(1,24): a + b + c = 24
(2,18): 4a +2b + c = 18
(3,2): 9a +3b + c = 2
----------------------------
Solve the system of equations be any method to get:
a = -5
b = 9
c = 20
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EQUATION:
y = -5x^2 + 9x + 20
======================
Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
This is distance, as a funtion of time
Here is the most general way to express it as a quadratic:

There are different snapshots of the dive, so that
should give me equations, and I should be able to
find , , and

Now figure out the square terms

I'll multiply the 2nd equation by , and the 3rd one by

Now subtract

Now subtract the 1st from the 2nd

Multiply by

Add

Subtract thre 3rd one from this

So, the equation I come up with is:

answer
Let's see if it satisfies the data given

OK

OK

OK
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