Hi,

 p(x) =  -x^2 + 812x - 9600 (graphically represents parabola opening downward



As the number of TV’s produced increases, what happens with the profit? 

 profit declines after the maximum profit is reached

How do you know how many solutions there are to the function? quadratic 2 sol.

Show how you determined the nature of the solutions using the Discriminant. 

    Positve value for discriminant:  real solutions





   x = (-812 ± 788)/-2

   x =  1600/2 = 800

   x =   24/2 = 12  Zero profit at 12 units and 800 units

How many TV’s must be produced to reach a maximum profit? 

Using the vertex form of a parabola,  where(h,k) is the vertex

 P(x) =  -x^2 + 812x - 9600 

 P(x) = -(x-406)^2 + 164836 - 9600  |completing the square

Vertex is at(406,155,236) the maximum point for the parabola. 

 maximum profit of 155,236 at 406 units produced.  

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