functions question (f.4 maths)@1

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)

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  • 1 decade ago
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    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

    =================================================

    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

    Source(s): me
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