Mathematically speaking the minimum and maximum (just like positive and negative) mean absolutely nothing, you'll realize this when you take university/college math courses or if you just think about it long enough.

Given the question however, it sounds like your in high school calculus.

The reason the y-value is called the minimum is because it is the lowest y-value that this function can obtain.

In other words, the lowest point on the line is at that same value of y, the "minimum" y-value.

The same goes for a parabaloid that opens downward only now that y-value is the highest y-value that the function is defined at (highest y-value for which there exists a point on the function).

Given the question however, it sounds like your in high school calculus.

The reason the y-value is called the minimum is because it is the lowest y-value that this function can obtain.

In other words, the lowest point on the line is at that same value of y, the "minimum" y-value.

The same goes for a parabaloid that opens downward only now that y-value is the highest y-value that the function is defined at (highest y-value for which there exists a point on the function).