Answer:
[tex]\large\boxed{g(x)=(x+1)^2+7=x^2+2x+8}[/tex]
Step-by-step explanation:
f (x) + n - shift up by n units
f (x) - n - shift down by n units
f (x - n) - shift to the right by n units
f (x + n) - shift to the left by n units
We have y = x² → f(x) = x². Shifted up by 7 units and to the left by 1 unit:
[tex]g(x)=f(x+1)+7=(x+1)^2+7[/tex]
use (a + b)² = a² + 2ab + b²
[tex]g(x)=x^2+2(x)(1)+1^2+7=x^2+2x+8[/tex]
