The graph of y=x^2 - 2x is at right. Use this graph and any other lines which you may need to add to it to solve the equations given. Briefly explain your method.
x^2 - 2x = 3
x^2 - 2x = x
In spite of substantial emphasis on viewing functions via multiple representations, students tend to have a favorite representation they revert to whenever possible. They often do not see the different representations of a function as carrying the same information and simply highlighting certain parts of it differently (e.g., x-intercepts).
Many students could not see how the graphs could help. Instead, students often attempted to solve the equation algebraically even though the given information is graphical.