Given quadratic function graph, determine function by using transformations

In this example problem, we are given the graph of a quadratic function and tasked with determining the function that would produce the graph. We identify the vertex on the graph and use transformations to come up with an initial function. We also include a variable to account for a stretch, compression, or vertical reflection. We then identify one additional point on the graph and substitute in the x-value and y-value into the function that we have formulated. This produced an equation with only one unknown variable. We solve for the remaining variable and then substitute it back into our initial function to complete the problem.