Final answer:
After correcting potential typos in the equation and assuming it to be quadratic, the vertex of y = -3x^2 + 12x - 8 is found using the vertex formula, producing the point (2, 4), which is not among the given choices.
Step-by-step explanation:
The equation provided by the student seems to have a typographical mistake as it combines terms consistent with a quadratic equation, -3x^2 for instance, but is missing the exponent. The correct form should likely be either y = -3x^2 + 12x - 8 for a quadratic equation or y = -3x + 12 - 8 for a linear equation. Assuming the former, to find the vertex of a quadratic function of the form y = ax^2 + bx + c, you can use the vertex formula where the x-coordinate of the vertex is x = -b/(2a). For the given equation, a = -3, and b = 12, so the x-coordinate of the vertex would be x = -12/(2*-3) = 2. Plugging this back into the equation, we find the y-coordinate: y = -3(2)^2 + 12*2 - 8 = -3*4 + 24 - 8 = -12 + 24 - 8 = 4. Thus, the vertex is at the point (2, 4), which is not listed in the provided options.