Answer:
The answer to your question is below
Explanation:
A) f(x) = x² + 4x + 1
Find the vertex
y = x² + 4x + 1
-Subtract 1 in both sides
y - 1 = x² + 4x
-Complete the perfect trinomial square in the right side
y - 1 + (2)² = x² + 4x + (2)²
-Simplify
y - 1 + 4 = (x + 2)²
y + 3 = (x + 2)²
-Find the vertex
V = (-2, -3)
B)
f(x) = x²
g(x) = (x - 4)² - 2 See the picture below
Shifted right 4 units
Shifted down 2 units