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小 發表於 2013-4-6 11:47 PM (第 4055 天)
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回覆 12# faifai219 的帖子
Let f(x) = 2x^2 – 8x + 9
Let g(x) = the quadratic equation with roots 3α – 2 and 3β – 2.
g(x) = f((x+2)/3) <--- WHY???
f(x) is transformed to g(x) by 2 steps.
(1) translate 2/3 unit to the left
h(x) = f(x+2/3)
roots of h(x): α – 2/3 and β – 2/3
(2) enlarge along the x-axis by 3 times
g(x)
= h(x/3)
= f(x/3 + 2/3)
= f((x+2)/3)
roots of g(x): 3(α – 2/3) and 3(β – 2/3), i.e. 3α – 2 and 3β – 2.
Think backward.
The two roots give you hints how to transform the graph.
[ 本帖最後由 n20311021 於 2013-4-6 11:48 PM 編輯 ]