High School Algebra Assignment

High school students solve quadratic equations using different methods, graph quadratic functions and identify key features of the graphs, and solve systems of linear and quadratic equations. The assignment is partially aligned to the standards. While it requires students to solve and graph some appropriately complex equations, it overemphasizes the use of specific solution methods, doesn’t involve complex solutions, and doesn’t ask students to interpret the key features of the functions they are asked to graph.

Focus 
Standard HSA.REI.B.4.B requires students to learn multiple methods for solving quadratic functions (taking square roots, completing the square, the quadratic formula, and factoring). This assignment gives students a chance to use a variety of those methods. However, the assignment also reinforces the idea that there is a “correct” method for solving certain types of quadratic functions. Although classroom discussions might focus on the type of quadratic function that lends itself easily to each method, the idea of a “correct” method is not a requirement of the standards.

Rigor
Standards HSA.REI.B.4.B and HSA.REI.C.7 require students to procedurally solve quadratic equations and systems of linear and quadratic equations, and this assignment allows them to do just that. However, there is an expectation that students will encounter complex solutions when solving, expressing them in the form a + bi (not addressed at all in this assignment), and that they will solve systems of one linear and one quadratic function (true for only two of the four systems in this assignment). Finally, the problems aligned with HSF.IF.B.4 do ask for some key information about the graph, but do not ask students to interpret these key features, as required by the standard.

Practice Standards
The assignment allows students to engage with Mathematical Practice Standard #1 (“Make sense of problems and persevere in solving them”) by solving systems of one linear and one quadratic equation—students must combine their understanding of how systems of equations operate with their understanding of solving for unknown values in a quadratic equation to solve for x and y. Students also have the opportunity to engage with Mathematical Practice #7 (“Look for and make use of structure”) when solving and graphing quadratic equations—students must understand how to find the key features of a quadratic graph from the equation or from an algebraic manipulation of the equation to an equivalent form.