Question

Describe how to obtain the graph of g(x)=(x+4)^2+2 +2 from the parent function f(x)=x^2

a.
4 units right and 2 units down
b.
4 units left and 2 units up
c.
4 units right and 2 units up
d.
4 units left and 2 units down

Answer 1

I think you added a 2 to g(x). Confirm, otherwise the equation of g(x) isg(x) =(x+4)² + 2 and f(x) = x²
Both g(x) and f(x) graphes re parabolas and have a standard form:
(y-k) = a(x-h)² , where h and k are the coordinates of the vertex V(h , k)

1st) f(x): (y+0) = (x+0)² →y= x² and the Vertex is the origine O(0,0)

2nd) g(x) = (x+4)² + 2 OR y = (x+4)² + 2 → (y-2) = (x+4)²:

So the vertex V has been moved downward by 2 units and to the left by 4 units.

CONCLUSION: 4 units left and 2 units down (Answer D)