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Math Help - need help with quadratic function

  1. #1
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    need help with quadratic function

    Identify vertex and x intercepts of quadratic function:
    f(x) = x^2 - 8x + 16

    Book's answer:
    f(x) = (x - 4)^2

    x intercept (4,0)
    vertex (4,0)


    The answer I came up with using f(x) = a(x - h)^2 + k :
    f(x) = 1(x^2 - 8x + 16) - (1)16 + 16
    f(x) = x^2 -8x + 16

    I tried strait factoring as well to find the x intercept but got nowhere.
    Any suggestions?
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  2. #2
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    Quote Originally Posted by dcd5105 View Post
    Identify vertex and x intercepts of quadratic function:
    f(x) = x^2 - 8x + 16

    Book's answer:
    f(x) = (x - 4)^2

    x intercept (4,0)
    vertex (4,0)


    The answer I came up with using f(x) = a(x - h)^2 + k :
    f(x) = 1(x^2 - 8x + 16) - (1)16 + 16
    f(x) = x^2 -8x + 16

    I tried strait factoring as well to find the x intercept but got nowhere.
    Any suggestions?
    f(x) is a perfect square, that is:  x^2 - 8x + 16 = (x-4)^2

    In the form f(x) = a(x-h)^2 + k = 1(x-4)^2 + 0

    The x intercept is where f(x) = 0 and so x=4

    The vertex is at (4,0) as this opens downwards and h = 4
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  3. #3
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    Quote Originally Posted by dcd5105 View Post
    Identify vertex and x intercepts of quadratic function:
    f(x) = x^2 - 8x + 16

    Book's answer:
    f(x) = (x - 4)^2

    x intercept (4,0)
    vertex (4,0)


    The answer I came up with using f(x) = a(x - h)^2 + k :
    f(x) = 1(x^2 - 8x + 16) - (1)16 + 16
    f(x) = x^2 -8x + 16

    I tried strait factoring as well to find the x intercept but got nowhere.
    Any suggestions?

    straight factoring will give you f(x) = (x - 4)^2 which is exactly what the book did
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