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Math Help - Quadrtaic Function word porblem

  1. #1
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    Quadrtaic Function word porblem

    Determine The Value of k so that y=5xsquared+100x+k has a maximum of 205

    I am really lost on this one
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  2. #2
    Raj
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    Put the equation into standard form then solve for k
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  3. #3
    Senior Member pacman's Avatar
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    nickdutta: "Determine The Value of k so that y=5xsquared+100x+k has a maximum of 205."

    The parabolic equation y = 5x^2 + 100x + k is a parabola opening upward,

    i think, 205 is the minimum. I will try solving it,

    y = 5x^2 + 100x + k

    completing the square,

    (y - k)/5 = x^2 + 20x + 100 - 100,

    (y - 5)/5 + 100 = (x + 10)^2

    (1/5)(y -(k - 500)) = (x + 10)^2,

    remember this standard equation of parabola?

    (x - h)^2 = (4p)(y - k)

    the vertex is (h, k) which is (-10, k - 500)

    Now the vertex has a coordinate of (-10, k - 500), where y = k - 500

    Now we have y = 205 as (STATED) maximum or minimum, then

    205 = k - 500,

    205 + 500 = k,

    705 = k,

    thus y = 5x^2 + 100x + 705.

    i made a graph,

    My solution looks awkward

    please double click the graph for a better view, any comment?

    anything wrong?
    Attached Thumbnails Attached Thumbnails Quadrtaic Function word porblem-frtg.gif  
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