Chapter 27: Graphing Quadratic Functions: Situation 21 From the MACMTL–CPTM Situations Project

When preparing a lesson on graphing quadratic functions, a student teacher found that the textbook for the class claimed that $x=-b2a$was the equation for the line of symmetry of a parabola y = ax² + bx + c. The student teacher wondered how this equation was derived.

This Prompt addresses graphing quadratic equations, specifically the derivation of the equation of the line of symmetry of a parabola. The Foci in this Situation deal with the general symbolic representation of a quadratic function, but they differ in the approaches used to obtain the equation in question. Focus 1 uses the symmetry of the parabola to find the x -coordinate of the vertex of the parabola. Focus 2 uses the first derivative to find the x -coordinate of the vertex of the parabola. Focus 3 utilizes transformations of the graph of y = x² to determine the coordinates of the vertex. Focus 4 uses some results about the roots of a polynomial equation, generally known as Viète's formulas, to find the x -coordinate of the vertex of the parabola.