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 = -b/(2a). If a > 0, f has a global minimum = -D/(4a) = (4ac-b^2)/(4a) at x = -b/(2a). If a < 0, f has a global maximum = -D/(4a) at x = -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 -D/(4a) gives the extreme value. For unrestricted domain, a > 0 means minimum only (no maximum), a < 0 means maximum only (no minimum).