This lesson is optional practice examining the effect of parameters in the vertex form of a quadratic expression on the graph of the function defined by the expression. Here, students think about how the structure of the form helps to explain these connections and helps to show whether the vertex of a graph represents the minimum or the maximum value of the function (MP7). They informally use the symmetry of the graph to locate two additional points on the graph to help them make a sketch.

Students are introduced to a more formal reasoning for why the sign of the quadratic coefficient determines whether the vertex is a maximum or a minimum. By examining the term in vertex form and using the fact that squared factors are always non-negative, students can see that the sign of determines whether the graph opens upward or downward.

Students are not assessed on this line of reasoning, but are prompted to apply their new insights to sketch the graphs of quadratic functions and to match a set of quadratic functions to the graphs that represent them.