The number of issues sold per month of a new magazine (in thousands) and its profit (in thousands of dollars) could be modeled by the function y = − 6x^2 + 36 x + 70. Determine the maximum profit in thousands of dollars.
recall that for any parabola y = ax^2+bx+c
the vertex is at x = -b/2a
So, all you need to do is find y when x = -36/-12 = 3
To determine the maximum profit, we need to find the vertex of the quadratic function. The vertex of a quadratic function y = ax^2 + bx + c is given by the formula:
x = -b / (2a)
In this case, the function is y = -6x^2 + 36x + 70, where a = -6, b = 36, and c = 70. Let's substitute these values into the formula:
x = -b / (2a) = -36 / (2*(-6)) = -36 / -12 = 3
Now that we have the x-coordinate of the vertex, we can substitute it back into the original function to find the corresponding y-coordinate:
y = -6(3)^2 + 36(3) + 70 = -54 + 108 + 70 = 124
Therefore, the maximum profit is $124,000.