Overview
In this unit, students will expand upon their knowledge of quadratic functions and equations. This will include graphing and transformations of equations, writing and solving equations in various ways, and modeling real-life situations. It is anticipated that this unit will take from six to eight weeks in a traditional hourly schedule.
Prior Knowledge
A.PA.08.02 For basic functions, e.g., simple quadratics, direct and indirect variation, and population growth, describe how changes in one variable affect the others.
A.PA.08.03 Recognize basic functions in problem context, e.g., area of a circle is ?r2, volume of a sphere is 4/3?r 3, and represent them using tables, graphs, and formulas.
A.RP.08.04 Use the vertical line test to determine if a graph represents a function in one variable.
A.RP.08.05 Relate quadratic functions in factored form and vertex form to their graphs, and vice versa. In particular, note that solutions of a quadratic equation are the x-intercepts of the corresponding quadratic function.
A.RP.08.06 Graph factorable quadratic functions, finding where the graph intersects the x-axis and the coordinates of the vertex; use words "parabola" and "roots"; include functions in vertex form and those with leading coefficient -1, e.g., y = x2 - 36, y = (x - 2)2 - 9; y = - x 2; y = - (x - 3)2.
A.FO.08.07 Recognize and apply the common formulas: (a + b)2 = a2 + 2ab + b2; (a - b)2 = a2 - 2ab + b2 ; (a + b)(a - b) = a2 - b2; represent geometrically.
A.FO.08.08 Factor simple quadratic expressions with integer coefficients, e.g.,
x2 + 6x + 9, x2 + 2x - 3, and x2 - 4; solve simple quadratic equations, e.g., x2 = 16 or x2 = 5 (by taking square roots); x2 - x - 6 = 0, x2 - 2x = 15 (by factoring); verify solutions by evaluation.