Illustrative Mathematics Student Workbook ~ Algebra 1 ~ Units 6 & 7

~ Unit 6 - Quadratic Functions ~ Model with quadratic functions. Construct quadratic functions and quadratic sequences. Describe properties that distinguish linear, exponential, and quadratic functions. Represent quadratic functions using recursive formulas, expressions, tables, and graphs. Find the average rate of change of a quadratic function over a unit interval, and compare rates for successive intervals. Express quadratic functions in equivalent forms; understand the relation between vertex form and the shape of the graph. ~ Unit 7 - Quadratic Equations ~ Connect solving quadratic equations to finding zeros of quadratic functions. Explore forms of quadratic equations that can be solved by seeing structure. Derive the equation of a parabola given the focus and a DirectX parallel to one of the axes. Express a quadratic function in the appropriate form for a given purpose, including vertex form. Solve problems using systems consisting of a linear and a quadratic equation in two variables. Understand and be able to use the method of factoring to solve factorable quadratic equations. Construct and solve quadratic equations by the most strategic method to solve problems in various contexts. Understand the method of completing the square to solve quadratic equations, and derive the quadratic formula.