The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero.
The y-intercept is the point at which graph crosses the y-axis.
The maximum value of a function is the place where a function reaches it’s highest point, or vertex, on a graph. If your quadratic equation has a negative a term, it will also have a maximum value. If you have the graph, or can draw the graph, the maximum is just the y value at the vertex of the graph.