Question 1002190: A dog toy is thrown from 5 inches above the ground. After 2 seconds, the toy reaches a maximum height of 9 inches, and then lands back on the ground 5 seconds after it was thrown. Find the "a" (coefficient of the x^2) and write this in quadratic equation in vertex form, standard form, and factored form.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A dog toy is thrown from 5 inches above the ground. After 2 seconds, the toy reaches a maximum height of 9 inches, and then lands back on the ground 5 seconds after it was thrown. Find the "a" (coefficient of the x^2) and write this in quadratic equation in vertex form, standard form, and factored form.
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Form:: h(t) = ax^2 + bx + c
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You have points (0,5),(2,9),(5,0)
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Using (0,5) you get: 0 + 0 + c = 5
Using (2,9) you get: 4a+2b + c = 9
Using (5,0) you get: 25a+5b+ c = 0
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Since c = 5 you get:
4a + 2b = 4
25a +5b = -5
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Modify for elimination:
2a + b = 2
5a + b = -1
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3a = -3
a = -1
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b = 2-2a = 2+2 = 4
c = 5
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Ans: h(x) = -x^2 + 4x + 5
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Cheers,
Stan H.
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