Answer: Graph Analysis:
The graph appears to be a parabola that opens upward, with a vertex at (2, 4). The parabola is shifted 2 units to the right, and the vertex is 4 units above the x-axis.
Matching the Graph with the Options:
Let's examine each option:
(A) f(x) = (x-2)^(2) + 4: This function would have a vertex at (2, 4), but it would not be stretched or shrunk. The graph appears to be stretched, so this option is unlikely.
(B) f(x) = 2(x+2)^(2) + 4: This function would have a vertex at (-2, 4), not (2, 4). So, this option is incorrect.
(C) f(x) = 2(x-2)^(2) + 4: This function would have a vertex at (2, 4) and would be stretched vertically by a factor of 2, which matches the graph.
(D) f(x) = -(x+2)^(2) - 4: This function would have a vertex at (-2, -4), not (2, 4), and would open downward, not upward. So, this option is incorrect.
Correct Answer:
The correct answer is:
(C) f(x) = 2(x-2)^(2) + 4
Step-by-step explanation:
