Determine g (x + a) - g (x) for the following function.

g (x) = - 5x^2-3x+2

g (x + a) - g (x) = ?

Easy

g (x+a)

sub x+a for every x in equation

g (x+a) = - 5 (x+a) ^2-3 (x+a) + 2

g (x+a) = - 5 (x²+2xa+a²) - 3x-3a+2

g (x+a) = - 5x²-10xa-5a²-3x-3a+2

so now minus g (x)

g (x+a) - g (x) =

-5x²-10xa-5a²-3x-3a+2 - (-5x²-3x+2) =

-5x²-10xa-5a²-3x-3a+2+5x²+3x-2=

-5x²+5x²-10xa-5a²-3x+3x-3a+2-2=

-10xa-5a²-3a

g (x+a) - g (x) = - 5a²-10xa-3a