A1.PAFR.2: Create, solve, and transform equations and inequalities in two or more variables to represent relationships between quantities and graph the equations on coordinate axes using appropriate labels, units, and scales.

Create, solve, and transform equations and inequalities in two or more variables to represent relationships between quantities and graph the equations on coordinate axes using appropriate labels, units, and scales.

A1.PAFR.2.1Transform linear, quadratic, exponential, and linear absolute value functions to equivalent forms to identify slope and y-intercept for linear, vertex, and roots (if any) for quadratic and linear absolute value, and y-intercept for exponential.A1.PAFR.2.2Solve quadratic equations by completing the square, factoring, and the quadratic formula, explaining the connection between the zeros of the function derived from the equation, its linear factors (if it factors), the x-intercepts of its graph (if they exist), and the solutions (if any) to the corresponding quadratic equation.A1.PAFR.2.3Solve and graph linear, quadratic, exponential, and linear absolute value equations given in tabular, symbolic, and/or verbal forms using intercepts, domain and range, intervals of increasing and decreasing, vertex (maximum and minimum), end-behavior, and symmetry, and interpret these in terms of mathematical and real-world situations.A1.PAFR.2.4Create, solve, and graph linear inequalities in two variables.A1.PAFR.2.5Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.A1.PAFR.2.6Create symbolic representations of linear and exponential functions, including arithmetic and geometric sequences, given graphs, verbal descriptions, and tables.A1.PAFR.2.7Use graphs to obtain exact and/or approximate solutions of equations, inequalities, and systems of linear equations in two variables (given or obtained by using technology).A1.PAFR.2.8Solve an equation of the form f(x) = g(x) graphically by identifying the x-coordinate(s) of the point(s) of intersection of the graphs of y = f(x) and y = g(x).A1.PAFR.2.9Solve systems of linear equations algebraically and graphically.A1.PAFR.2.10Analyze the growth/decay rate between linear and exponential functions specifically between consecutive integers.

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