A firm maximises profitt at 5 units, breakeven at 8 units, but loses 10 000 if nothing is sold, determine the quadratic function relating to units sold.

Starting with the general form of the quadratic equation:



what you want to do is determine values for b and c in terms of a, then solve for a.

From the first condition you know that the derivative of y equals zero at x = 5


Therefore

So now you can substitue for b in the basic quadratic equation.

The second piece of information you were given tells you that the value of y is 0 at x = 8, so:



From this you can express c in terms of a.

Finally the last condition tells you that y(0) = -10000. From this you can now determine the value of a.

Hope this helps.