FJHS Algebra 1: Solving Quadratic Equations

It's critical for students to see the need for solving quadratic equations. The bridge from graphing quadratic functions to solving quadratic equations naturally builds from the application of projectile motion. If students consider the key features within the context of projectile motion, they will quickly see the need for solving a quadratic equation to find the x-intercept(s) and the need to find the vertex of a quadratic function written in standard form. Encourage students to become fluent with all solving methods and leverage the power of which method is most effective for different scenarios.

The following unit progression stems from comparing vertex form and standard form in the context of projectile motion. Students quickly decide vertex form is their form of preference, but reality hits hard when most application settings model standard form equations. This series of activities begins with an adventure of modeling standard form equations as a square (vertex form) or rectangle (intercept form) with algebra tiles. Students discover the methods of completing the square and factoring but find more benefit in completing the square. However, they grow tired of the ugly fractions that ensue and beg for a generalized version (aka the quadratic formula) to reduce the mess. And this also expands options for graphing a quadratic function in standard form. Visit College Preparatory Mathematics for a Water Balloon Contest task (see pages 14 and 17) to assess understanding of quadratics.