Question

What is the rang y=-x2 - 2x + 3?​

Answer 1

This is a downward facing parabola, so its range comes in the form

$(-\infty, m)$ where m is the y coordinate of the vertex of the parabola.

We can find the x coordinate of the vertex using

$x=-\dfrac{b}{2a}=-\dfrac{-2}{-2}=-1$

And if we plug -1 in the equation we get the y coordinate of the vertex:

$y=-(-1)^2-2(-1)+3 = -1+2+3=4$

So, the range is the interval

$(-\infty, 4)$