Final answer:
The expression −x^2−4y^2+2x−12y−10 represents a parabolic shape in two variables and does not have a highest value without additional constraints.
Step-by-step explanation:
The expression −x^2−4y^2+2x−12y−10 does not have a highest value in the traditional sense because it represents a quadratic equation in two variables (a parabola in 3 dimensions, specifically). However, it is similar to one of a parabolic shape opening downward, which would generally have a maximum point at its vertex. Since the question does not specify a particular domain or range (and the variables can take any real values), we cannot find a maximum value in this case. It is important to note that the provision of the quadratic equation at² + bt + c = 0 and the corresponding values of a, b, and c in the reference information appears to be extraneous and not directly related to the original question about the expression's highest value.