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    Functions and Parabolas : Intercepts, Vertex, Line of Symmetry and Image Set

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    This question concerns the parabola which is the graph of the function: f(x) = [1/4(x-2)^2] -1
    a) Explain how the graph of the parabola can be obtained from the graph of y =x[squared] by using appropriate translation and scalings.

    b) Using your answer to part (a), or otherwise, write down the coordinates of the vertex of the parabola.

    c) Find the x-intercepts and the y-intercept of the parabola.

    d) Sketch the parabola, giving the coordinates of the vertex and of the points at which the graph crosses the axes.

    e) Write down the equation of the axis of symmetry of the parabola.

    f) What is the image set of the function f? (you should express your answer in interval notation)

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    Solution Preview

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    a) From the graph of , we can obtain by the following steps.
    Step 1: Move to the right by 2 units and get
    Step2: ...

    Solution Summary

    Intercepts, Vertex, Line of Symmetry and Image Set are found for a parabola. The graph is also drawn. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.