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Math Help - graph transformation

  1. #1
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    graph transformation


    Suppose the graph of y=x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?
    (a)
    (b)
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  2. #2
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    Quote Originally Posted by harry View Post

    Suppose the graph of y=x^2 is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph?
    (a)
    (b)
    When you translate a coordinate, say x, you replace it with a shifted value in the "opposite" direction.

    In the case of a) you are shifting the parabola down by 3, so we need to add 3 to the y-coordinate:
    y = x^2 \to y + 3 = x^2
    or
    y = x^2 - 3

    In the case of b) you are shifting the parabola 4 units in the +x direction, so you want to subtract 4 from the x coordinate.
    y = x^2 \to y = (x - 4)^2

    -Dan
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