functions question (f.4 maths)@1

missyoou_forever

2007-10-16 8:01 am

1.A quadratic function f(x) is transformed to another quadratic function g(x)=x^2-4x+5 by translation.Given that the vertex of the graph of y =f(x) is (-2,1),find the symbolic repressentation of f(x)

回答 (1)

2007-10-16 8:33 am

✔ 最佳答案

g(x) = x^2 - 4x + 5
= (x - 2)^2 + 1 by completing square
所以g(x) 個vertex 係 (2,1)
相對於 f(x) 個vertex 係 (-2,1)
so g(x) 係 f(x) 既 horizontal translation
打橫translate左4格

let x' 做 f 既x-axis variable
而 x 做 g 既x-axis variable
咁 x' = x + 4

so 將 g(x) 入面既 x, 改哂做 x', 得到f(x)
f(x) = (x')^2 - 4(x') + 5
= (x + 4)^2 - 4(x + 4) + 5
= x^2 + 8x + 16 - 4x - 16 +5
= x^2 + 4x + 5

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check數:
將f(x) 做completing square
f(x) = (x + 2)^2 - 4 + 5
= (x + 2)^2 + 1
岩岩好, 係(-2,1) 有個vertex

參考: me

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