the quadratic function f is defined as f (x) = -(x + 2)^2 + 3 consider the graph of y equals f(x) in the xy-plane. state whether there is a possible transformation of f in the form g(x) = f(x) + k, where k is a constant, for which the graph of y = g(x) will have no x-intercepts. justify your answer.
No, there is not a possible transformation of f in the form g(x) = f(x) + k, where k is a constant, for which the graph of y = g(x) will have no x-intercepts. This is because the graph of y = f(x) already has no x-intercepts, so any transformation of the form g(x) = f(x) + k will still have the same x-intercepts as the original graph.
