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    Plot f(x)=3(x-7)^2+5 using transformations. Track the points (0,0)(1,1) and (-1,1) from the reference equation (graph) to their final position.

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    Solution Preview

    The reference equation, or graph, is a parabola corresponding to f(x) = x^2, with the minimum at (0,0). For convenience, we will call this f(z) = z^2, so as not to confuse the two variables, and handle each transformation as a modification to the function f(z). (See Figure 1 (a))
    The relevant transformations in this case are:
    z = x-7 shifts the graph 7 to the right, because to give the equivalent value for f(x), and by ...

    Solution Summary

    This shows how to plot a function using transformations. The expert graphs final positions of reference equations.