The percent of a​ country's population that is foreign born can be modeled by the equation yequals0.006xsquaredminus0.412xplus19.916​, where x is the number of years after 1900.
a. Is the vertex of the graph of this function a maximum or a​ minimum?
b. Assuming that the pattern indicated by this model remains the​ same, find the input and output at the vertex.
c. Interpret the results of part b.
d. Use the vertex to set the window and graph the model.