HSA-CED.A
Create equations that describe numbers or relationships.

HSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

HSA-CED.A.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

HSA-CED.A.3
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

HSA-CED.A.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

HSA-REI.B.4
Solve quadratic equations in one variable.

HSA-REI.B.4.a
Use the method of completing the square to transform any quadratic equation in into an equation of the form that has the same solutions. Derive the quadratic formula from this form.

HSA-REI.B.4.b
Solve quadratic equations by inspection (e.g., for ), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as for real numbers and .

HSA-SSE.B
Write expressions in equivalent forms to solve problems.

HSA-SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

HSA-SSE.B.3.a
Factor a quadratic expression to reveal the zeros of the function it defines.

HSA-SSE.B.3.b
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.HSF-IF.B
Interpret functions that arise in applications in terms of the context.

HSF-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

HSF-IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function gives the number of person-hours it takes to assemble engines in a factory, then the positive integers would be an appropriate domain for the function.

HSF-IF.B.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.

HSF-IF.C
Analyze functions using different representations.

HSF-IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

HSF-IF.C.7.a
Graph linear and quadratic functions and show intercepts, maxima, and minima.