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.