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 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 constant, for which the graph of y = g(x) will have no x-intercepts. This is because the graph of y = f(x) has two x-intercepts, which means that the graph of y = g(x) will always have at least two x-intercepts, regardless of the value of k.
