Whoever answers this, can you explain how you did it, like I know this is easy stuff but I dont understand the way my teacher does it.

f(x)    =  1x^2  + 4x   - 5

The form is    f(x)  = ax^2 + bx + c

This is a polynomial.....a polynomial always has a domain of  all real numbers  (it is continuous  on the x axis )

This si a parabola that turns upward.....we  can find  the  x value that  gives a minimum  by

-b/ (2a)   = -4 / ( 2 (1)  =   -2

To find the  y value  for this x

1 (-2)^2  + 4(-2)  - 5  =   4 - 8  - 5   = -9

1 is the  minimum value in the range....and  there is no max  ( the function continues "upward" forever )

So....the range is  [ -9, infinity  )