Creating a Concave Down Quadratic with a Predetermined Vertex

by Amy Benson

We begin with the reminder that our original equation is

and that the graphing form of this equation is

To create a concave down equation, we need to change a = 2 to a = -2 remembering that the general graphing form of a quadratic is

Our new equation is

Let's compare the graphs the original equation and our new equation

What would the new equation look like in standard form?

In this form, we cannot immediately see that our new equation shares its vertex with the original equation, however we have shown that it does.

Classroom Tip: Students are more likely to guess and check than to systematically work through the above steps. It is important to stress the equations and how they relate to the graphs.