Final answer:
The correct graph is of the function f(x) = -x² + 2x + 4, which has a maximum due to the negative coefficient of x² and a y-intercept of 4, verified by evaluating f(0) = 4.
Step-by-step explanation:
The student asks for the graph of a function that has a maximum and a y-intercept of 4. The function with these characteristics is f(x) = -x² + 2x + 4. This is a quadratic function where the coefficient of x² is negative, indicating that the graph opens downwards and therefore has a maximum point. The y-intercept can be found by evaluating the function when x is equal to 0, which leads to f(0) = 4, confirming the y-intercept at 4.
To illustrate this, graphing the function would involve plotting points and using the vertex formula or completing the square to find the vertex, which represents the maximum point. It's important to note that the other functions listed do not meet the conditions because they either have the wrong y-intercept or they do not have a maximum point (for example, function 4 opens upwards).