Final answer:
The given expression represents a quadratic function with a maximum value. The maximum occurs at x = 0, not x = 2.
Step-by-step explanation:
The given expression -3(x+2)^2 - 250 represents a quadratic function. To determine whether it has a maximum or minimum value and at what x-coordinate, we can analyze the coefficient of the squared term (a) and its sign. In this case, a = -3, which is negative. This means that the graph of the quadratic function opens downwards, indicating a maximum value.
We can also find the x-coordinate of the maximum by using the formula x = -b/2a. In the given expression, b = 0 and a = -3. Substituting these values into the formula, we get x = -0/2(-3) = 0. Therefore, the expression has a maximum value at x = 0.
Therefore, the correct answer is a) A maximum of 250 at x = 2 (since the maximum value occurs at x = 0, not x = 2).