Algebra 2; interval decreasing, parabola.?

If f(x) = -1/2(x-2)^2 +7, on what interval is f(x) deccreasing? How can you do this WITHOUT a calculator.

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  • 8 years ago
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    The (-1/2) in front of the (x-2)^2 part tells you that it is a downwards-opening parabola.

    From the (x-2)^2 part, you know that x = 2 is the x-coordinate of the vertex. You can figure out the y-coordinate of the vertex, because it is f(2) = 7. The vertex is (2,7) .

    So you are (imagining) looking at a downwards-opening parabola with vertex (2,7) as you look (in your mind) at the graph. As x goes from left to right, the graph rises from negative infinity to the vertex (2,7) , and then falls to negative infinity again as x moves to the right of 2 towards positive infinity.

    The function is therefore decreasing on the interval ( 2 , + infinity )

    ---------------

    Here's the graph of the function. (And I sure hope it bears out what I just said above, because I didn't graph it beforehand lol) :

    (it did :)

    http://s1164.photobucket.com/albums/q561/iago9/?ac...

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