SOLUTION: Please help me! Thanks (: Approximate the zeros of the function. Round to the nearest tenth. 1.) y=x^2-7x+7 2.) y=-2x^2-9x+10

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Question 1028737: Please help me! Thanks (:

Approximate the zeros of the function. Round to the nearest tenth.

1.) y=x^2-7x+7

2.) y=-2x^2-9x+10


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
We use Newton's method to approximate zeros
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x(n+1) = x(n) - (f(x(n)) / f'(x(n)))
:
1) y = x^2-7x+7
Consider the graph of this equation
+graph+%28+300%2C+200%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-7x%2B7%29+
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The zeros are close to 1 and 6, I will show you how to find the zero close to 1. All others follow the same procedure.
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Calculate f'
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f' = 2x-7
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Let x(0) = 1, then
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x(1) = x(0) - (f(x(0)) / f'(x(0))
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x(1) = 1 - (1 / -5) = 1.2
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x(2) = 1.2 - (0.04 / -4.6) approx 1.2
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Since x(2) = x(1), there is no point in continuing
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f(1.2) = 0.04 approximately 0.0, therefore
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x = 1.2 is a good approximation for a zero
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