I don't have a calculator near me... but you probably do. So just plug in those values for t.
Y = 4(-3) ^2 + 5
(Actually.. I might be able to do these in my head...) Y = 41
Y = 4(-1.5) ^2 + 5
Y = 14
Y = 4(0) ^2 + 5
Y = 5
Y = 4(1) ^2 + 5
Y = 9
Y = 4(4) ^2 + 5
Y = 69
The range is all the Y values. So it would be {41, 14, 5, 9, 69}