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Analyzing Quadratic Functions

describe how the graphs of the following functions relate to the graph of y=x^2.

Could someone please tell me what that means? I sort of understand it, but I want to get it perfectly straight.

y = (x+5)^2

Since it's in the brackets, that would mean go five units horizontally. And would it go negative because doesn't it go in the opposite direction?:S

y = x^2-7. Is -7 the slope?

y = 5+(x-2)^2. This one is confusing.

  • Math -

    You are correct on the first one. The new function is x^2 if we use a value 5 less than originally. That is, the graph is shifted 5 units to the left.

    y = x^2 - 7

    is just the graph of y=x^2, but shifted down 7 units.

    Now you come upon shifting in both directions.

    shift 2 units right, then 5 units up.

    In general, the graph of y = f(x) is shifted h units to the right and k units up if

    (y-k) = f(x-h)

    You can see that the new function is just f(x) if we adjust the values of x and y by h and k, respectively.

  • Math -

    If you want to play around with graphs, go to

    rechneronline dot de slash function-graphs

    You can type in a function f(x) of your choosing (they start out showing x^2). Then, just substitute (x-2) for x and see how the graph shifts.

    It's also cool because you can show both graphs at once, in different colors.

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