the function g has defining equation?

Question

the function g has defining equation g(x)=x^2 - 3x + 2 find and simplify (g(4+h)

Answer 1

if g(x)=x^2 - 3x + 2
and x = 4 + h, then you first plug in 4 + h for x:
g(4 + h) = (4 + h)^2 - 3(4 + h) + 2

Distribute into the parenthesis:
g(4 + h) = (h^2 + 8h + 16) - (12 + 3h) + 2

Simplify:
g(4 + h) = h^2 + 8h + 16 - 12 - 3h + 2
g(4 + h) = h^2 + 5h + 6 (solution!)