The offenders here are the ordered pairs (-2, 1) and (-2, 2). With any function we only want to get out <em>one specific</em> output (in the range) for any one input (in the domain). If you fed this function a -2 as input, it wouldn't know whether to give you out a 1 or a 2! This property - one input in, one output out - is essential for a function, so the relation shown does <em>not </em>describe one.
4m^2+3m-1=0
a=4
b=3
c=-1
input
x= 
x= 
x= 
x= 
x= 
or 
x=-1 or 1/4