Cue Column:

• When does f(x) have a minimum?
• When does it have a maximum?
• What is the extremal value?

Note Column: f(x) = $ax^2$ + bx + c: The vertex is at x = -$\frac{b}{2a}$. If a > 0, f has a global minimum = -$\frac{D}{4a}$ = $\frac{4ac-b^2}{(4a)}$ at x = -$\frac{b}{2a}$. If a < 0, f has a global maximum = -$\frac{D}{4a}$ at x = -$\frac{b}{2a}$. On a restricted interval [p,q], evaluate f at both endpoints and at the vertex (if vertex is in [p,q]).

Summary: The vertex formula -$\frac{D}{4a}$ gives the extreme value. For unrestricted domain, a > 0 means minimum only (no maximum), a < 0 means maximum only (no minimum).