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For the expression −x^2−4y^2+2x−12y−10, what is the highest value?

a) -10
b) 10
c) 20
d) 30

1 Answer

3 votes

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.

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