Question

The parabola y=x^2 is shifted up by 7 units and to the left by 1 unit.

Answer 1

Answer:

$\large\boxed{g(x)=(x+1)^2+7=x^2+2x+8}$

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:

$g(x)=f(x+1)+7=(x+1)^2+7$

use (a + b)² = a² + 2ab + b²

$g(x)=x^2+2(x)(1)+1^2+7=x^2+2x+8$