Given g(x)= -x^2 +9 Find g(x-5)

Question

I think I have the right anwser, but would oike clarification on the work behind it.

Answer 1

 

g(x-5) = -(x-5)^2 + 9

 

          =  -(x^2 - 10x + 25) + 9

 

         = -x^2 + 10x - 25 + 9

 

          = -x^2 - 10x - 16

 

         = -(x^2 + 10x + 16)

 

        = -(x     +   8 )( x  +     2   )

 

 

CHECK:

  pick x = 10

  then g(x) = g(10) = -10^2 + 9 = -100 + 9 = -91

 

  g(x-5) = g(5) = -5^2 + 9  = -25 + 9 = -16

 

  NOW:  -(5+8)(5+2) = -13*7 = -91 using the ANSWER that we found in bold above

 

THAT shows the answer is correct