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Math Help - concerning the graphs of a function

  1. #1
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    concerning the graphs of a function

    f(x)= 1/4(x-2)^2-4

    how can the parabola that is the graph of f be obtained from the graph of y=x^2

    what are the co-ordinates of the vertex of the parabola?

    what are the x-intercepts and the y-intercepts of the parabola?

    what is the image set of the function in interval notation?
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  2. #2
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    Graphical interpretation of Transformation of a function

    Hello loes
    Quote Originally Posted by loes View Post
    f(x)= 1/4(x-2)^2-4

    how can the parabola that is the graph of f be obtained from the graph of y=x^2
    The graph of f(x - a) is the graph of f(x) shifted to the right a units.

    The graph of kf(x) is the graph of f(x) stretched parallel to the y-axis with factor k.

    The graph of f(x) - b is the graph of f(x) shifted downwards b units.

    Put these three facts together, and you can describe how the graph of y=\tfrac{1}{4}(x-2)^2 - 4 is obtained from the graph of y = x^2.

    what are the co-ordinates of the vertex of the parabola?
    Where is the vertex of y = x^2? So where will it end up when you apply all three of these transformations?

    what are the x-intercepts and the y-intercepts of the parabola?
    The x-intercepts are the values of x that satisfy \tfrac{1}{4}(x-2)^2 - 4=0.

    The y-intercept is the value of y when x = 0.

    what is the image set of the function in interval notation?
    What is the image set for y = x^2? What will happen to this set when the transformations are applied?

    Grandad
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