SOLUTION: {{{y=x^2-4x-5}}} please put the function in the form {{{y=a(x-h)^2+k}}} what is its line of symmetry? how it compares to graph of {{{y=x^2}}} ?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: {{{y=x^2-4x-5}}} please put the function in the form {{{y=a(x-h)^2+k}}} what is its line of symmetry? how it compares to graph of {{{y=x^2}}} ?      Log On


   

Question 24542: y=x%5E2-4x-5 please put the function in the form y=a%28x-h%29%5E2%2Bk
what is its line of symmetry?
how it compares to graph of y=x%5E2 ?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Y=X^2-4X-5={(X-2)^2-4-5}=(X-2)^2-9
COMPARING WITH THE GIVEN EQN .
y=a%28x-h%29%5E2%2Bk,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%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-4x-5%2C+x%5E2%29+
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