Describe the relationship between the graph of \( f(x) = x^2 \) and the graph of \( g(x) = (x - 4)^2 + 3 \).
A. They are exactly the same function.
B. The graph of \( g(x) \) looks exactly like the graph of \( f(x) \), but it has been moved 3 units to the right and 4 units up.
C. The graph of \( g(x) \) looks exactly like the graph of \( f(x) \), but it has been moved 4 units to the left and 3 units up.
D. The graph of \( g(x) \) looks exactly like the graph of \( f(x) \), but it has been moved 4 units to the right and 3 units up.
Answer (2)
F(x)=x^2 is a basic parabola G(x)=(x-4)^2+3 is a shifted parabola The -4 in g(x) means move to the right 4 units The +3 means move up 3 units Final answer: Choice D, 4 units to the right and 2 units up
The graph of g ( x ) = ( x − 4 ) 2 + 3 is derived from the graph of f ( x ) = x 2 by shifting it 4 units to the right and 3 units up. Therefore, they share the same shape, making the correct answer choice D. The vertex of g ( x ) is at (4,3) compared to the vertex of f ( x ) at (0,0).
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