Parent Graphs and Transformations

Students learn that the parent graph of a linear relationship is y = x, which is a diagonal line that passes through the origin, and the parent graph of the family of quadratic functions is y = x^2, which is a parabola that opens upward and whose vertex is the origin. When a constant is added to a parent term - for example, when y = x is changed to y = x + 2 - the new graph is translated 2 units up from the parent graph. When a parent term is multiplied by a constant that is greater than 1 or less than negative 1 - for example, when y = x^2 is changed y = 3x^2 - the new graph is steeper than the parent graph.