Question 24542
Y=X^2-4X-5={(X-2)^2-4-5}=(X-2)^2-9
COMPARING WITH THE GIVEN EQN .
{{{y=a(x-h)^2+k}}},WE INFER THAT 
A=1,H=2 AND K=-9....THE LINE OF SYMMETRY IS X-2=0 AS YOU WILL GET SAME VALUE OF Y WHETHER X-2=+4 SAY OR -4...NAMELY,Y=7.
COMPARISON WITH Y=X^2 IS SHOWN BELOW 
 {{{ graph( 600, 600, -10, 10, -10, 10, x^2-4x-5, x^2) }}}
YOU CAN SEE THAT LINE OF SYMMETRY IS X=0 HERE.
ALSO THE MINIMUM VALUE OR VERTEX AT 0,0 IN CASE OF Y=X^2,WHERE AS IT WAS AT (2,-9)
FOR THE GIVEN EQUATION