Question

given the function y=-3(x-1)^2 -4, how do i find the range?

Answer 1

$The vertex form:\ y=a(x-p)^2+q\ where\ (p;\ q)-coordinates\ of\ the\ vertex$

The range of function $y=ax^2+bx+c$

if a > 0 then the range R = [q; ∞)
if a < 0 then the range R = (-∞; q]

We have: $y=-3(x-1)^2-4\\\\a=-3 < 0\ and\ q=-4$

therefore the range $R=(-\infty;-4]$