SOLUTION: If the function G(x) = (x - 8)2 + 6 has the same shape as F(x) = x2 + 6, how far to the right of F(x) is G(x) shifted?

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Question 176630: If the function G(x) = (x - 8)2 + 6 has the same shape as F(x) = x2 + 6, how far to the right of F(x) is G(x) shifted?
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
i presume you mean %28x-8%29%5E2 and x%5E2
f%28x%29+=+x%5E2+-+6
g%28x%29+=+%28x-8%29%5E2+-+6
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when x = 0, g(x) = (-8)^2 - 6 = 64 - 6 = 58
when x = 0, f(x) = (0 - 6 = -6
when f(x) = -6, x = 0
when g(x) = -6, x = 8
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one of the general forms of quadratic equation is:
f%28x%29+=+a%28x+-+h%29%5E2+%2B+k
or
g%28x%29+=+a%28x+-+h%29%5E2+%2B+k
where (h,k) is the vertex which is the turning point of the equation.
with f(x), h was 0 and k was -6
with g(x), h was 8 and k was -6
looks like g(x) was shifted 8 units to the right.
graph of both equations follows:
f(x) is -6 when x = 0
g(x) is 58 when x = 0
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graph%28800%2C400%2C-5%2C15%2C-10%2C100%2C%28x-8%29%5E2-6%2Cx%5E2-6%29