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Math Help - problem solving for a test tomorrow!!!

  1. #1
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    Exclamation problem solving for a test tomorrow!!!

    A company first started recording their profit making in december 2007, before the financial crisis. They recorded it quarterly for 2 years. It is recorded in 1000's dollars.
    P(t) = t^2-9t+14

    (x intercepts: 2 and 7)
    (y intercept: 14)
    (vertex: 4.5, -6.25)
    Questions:
    1) When the company recorded its lowest profit, what quarter did this happen in?

    2) when did there profit first start to rise?

    3) Find P(t) when t=0

    4) When did the profit reach 20 000 dollars?

    5)calculate k if the company made no loss.
    P(t) = t^2-9t+14+k
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  2. #2
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    is t years?
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  3. #3
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    T isn't years, its for the quarterly times.

    T is the x asis, and the y axis is for the profit.
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  4. #4
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    oh ok, my apologies. i was unclear.

    1) the lowest profit would occur at the vertex, so 4.5, which i assume would be part of the first quarter of the second year.

    2) the profit first started to rise right after the vertex, after x=4.5, but it didnt actually become positive until the x-intercept x=7

    3) P(t)=t^2-9t+14

     P(0)=(0)^2-9(0)+14

    P(0)=14

    4) 20=t^2-9t+14

     <br />
0=t^2-9t-6<br />

     <br />
\frac{-b+/-\sqrt{b^2-4ac}}{2a}<br />

     <br />
\frac{9+\sqrt{(-9)^2-4(1)(-6)}}{2(1)}<br />

     <br />
\frac{9+\sqrt{81+24}}{2}<br />

     <br />
\frac{9+\sqrt{105}}{2}<br />

     <br />
x=9.623ish<br />

    so since this is only for the first two years, the profit has not reached $20,000 yet.

    5) im not sure what exactly part 5 means.sorry
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  5. #5
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    Thank you so much !
    Im sorry the information i gave was so sketchy, we had a test today and it was all i cold remember of the question i didnt understand.
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