Answer:
the answer is B (0, -2)
Explanation:
To find the point on the curve y = -x^2 - 2 that is closest to the point (0,1), we can use the method of least squares.
The method of least squares involves finding the point on the curve that minimizes the square of the distance between the point and the curve.
To begin, we can define a function d(x) = (y - (-x^2 - 2))^2 which represents the square of the distance between the point (x,y) on the curve and the point (0,1)
then we need to find the derivative of d(x) and set it to zero to find the minimum,
d'(x) = 2(y + x^2 + 2 - 1) = 2(y + x^2 + 1)
by setting d'(x) = 0 we get y = -x^2 - 1,
so the point on the curve that is closest to (0,1) is (0, -1) and the answer is B (0, -2)
Note that the point (0,-1) is on the curve y = -x^2 - 2 but not the point on the closest.