To find the price at which the company should sell the video game to maximize profit, we need to find the vertex of the quadratic function y = -x^2 + 89x - 747.
The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the formula:
Vertex = (-b/2a, c - b^2/4a)
Substituting the values from the given equation, we get:
Vertex = (-89/2*-1, -747 - 89^2/4*-1)
Solving for the x-value of the vertex, we get:
x = 44.5
Therefore, the video game should be sold for $44.50 to maximize profit.