What is the range of y= -x^2+2x-3

Question

Im being asked to display in point builder notation and set interval and i dont quite under what that means

Answer 1

y=-x²+2x-3 can be written: 

y=-3-(x²-2x+1-1), y=-3-((x-1)²-1)=-3+1-(x-1)²=-2-(x-1)². (A parabola (inverted U-shape) with vertex at (1,-2).)

A square has a least value of zero so y cannot be more than -2. This helps us to define the range.

For all other values of x, y will be less than -2. So the range is (-∞,-2] (semi-infinite). The interval is shown in set builder notation. This can be written y∈(-∞,-2] for x∈(-∞,∞).