Quadratic functions
A parabola turns around exactly once. What do that turning point and the intercepts say about a function’s outputs, and about the situation it describes?
Where you are 3 inside
What this area is about
A quadratic function has the form f(x) = ax^2 + bx + c with a \ne 0. Its graph is a parabola that opens up when a > 0 and down when a < 0. The algebra of parabolas, such as the vertex and axis of symmetry and factored form, comes earlier. This area reads those features as facts about a function: its outputs, its range, and what it says about a real situation.
How these fit together
Choosing a form. Reading a quadratic in its three forms shows which of standard, vertex and factored form answers a given question, and compares two quadratics given in different ways.
A result about outputs. Maximum, minimum and range uses the vertex: it gives the smallest output when a > 0 and the largest when a < 0, and that fixes the range.
Applications. Quadratic functions in context says what the intercepts, the vertex and the axis of symmetry mean, with units, for areas, profits and thrown objects.
A path through it
The three forms first, then maximum, minimum and range, then context, which needs the vertex as a highest or lowest point.
A quadratic is also the degree 2 case of the polynomial functions, whose shapes are treated in general in their own area.