Students investigate quadratic functions in terms of standard, vertex and factored form and what those forms tell us about the graph and solutions to quadratic equations. Students write equations from graphs and vice versa. Also included is the second constant term using finite differences, the general pattern of all quadratic graphs, domain and range, how to find the vertex from standard form without completing the square, and solving equations in the form of 0 = x^2 and those requiring the quadratic formula.
NOTE: The treatment of imaginary numbers here is not intended to be complete. It is introduced only as a context for graphs that do not cross the x-axis and using the quadratic formula.