What function should be used to minimize the distance between and the point (2, 0)?

for any point on the curve, the distance z to (2,0) is

z^2 = (x-2)^2 + (y-0)^2
= x^2-4x+4 + x+3
= x^2-3x+7

so, use z = √(x^2-3x+7)

you dropped something out

Yes! Sorry! y=sqrt of (x+3)

To minimize the distance between a point and another point, we can use the concept of distance or "Euclidean distance" in mathematics. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the point is not specified, so we can denote it as (x, y). The given point is (2, 0). We want to minimize the distance between and (2, 0). Therefore, we need to minimize the distance using the formula mentioned above.

In mathematical terms, we can define a function for the distance between and (2, 0) as:

f(x, y) = √((2 - x)^2 + (0 - y)^2)

To find the point (x, y) that minimizes this distance, we can apply optimization techniques such as taking partial derivatives and solving for critical points. However, without further context or constraints, it's not possible to determine an exact solution.

Overall, the function to minimize the distance between and the point (2, 0) is f(x, y) = √((2 - x)^2 + (0 - y)^2).