
Seeing Structure in ExpressionsASSE Interpret the structure of expressions.MGSE912.A.SSE.2 Use the structure of an expression to rewrite it in different equivalent forms.Show detailsASSE Write expressions in equivalent forms to solve problems.MGSE912.A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties
of the quantity represented by the expression.MGSE912.A.SSE.3a Factor any quadratic expression to reveal the zeros of the function defined by
the expression.MGSE912.A.SSE.3b Complete the square in a quadratic expression to reveal the maximum or
minimum value of the function defined by the expression.Creating EquationsACED Create equations that describe numbers or relationships.MGSE912.A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
Include equations arising from linear, quadratic, simple rational, and exponential functions (integer
inputs only).MGSE912.A.CED.2 Create linear, quadratic, and exponential equations in two or more variables to
represent relationships between quantities; graph equations on coordinate axes with labels and scales.
(The phrase “in two or more variables” refers to formulas like the compound interest formula, in which
A = P(1 + r/n)nt has multiple variables.)Reasoning with Equations & InequalitiesARE I Solve equations and inequalities in one variableMGSE912.A.REI.4 Solve quadratic equations in one variable.MGSE912.A.REI.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^{2} = q that has the same solutions. Derive the quadratic
formula from ax^{2} + bx + c = 0.MGSE912.A.REI.4b Solve quadratic equations by inspection (e.g., for x^{2} = 49), taking square roots, completing the square, and the quadratic formula, as appropriate to the initial form of the
equation (limit to real number solutions).GA: HS: FunctionsInterpreting FunctionsFIF Interpret functions that arise in applications in terms of the context.MGSE912.F.IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.FIF Analyze functions using different representations.MGSE912.F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.MGSE912.F.IF.8a Use the process of factoring and completing the square in a quadratic function toShow details
show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.MGSE912.F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).Show detailsBuilding FunctionsFBF Build a function that models a relationship between two quantities.MGSE912.F.BF.1 Write a function that describes a relationship between two quantities.FBF Build new functions from existing functions.MGSE912.F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Key Vocabulary Complete Factorization • Completing the Square • Difference of Two Squares • Discriminant • Horizontal Shift • Perfect Square Trinomial • Quadratic Equation • Quadratic Function • Root • Standard Form of a Quadratic Function • Vertex • Vertex Form of a Quadratic Function