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US-VA

Math

Virginia Math

Algebra 2: Equations and Inequalities

A2.EI.1

The student will represent, solve, and interpret the solution to absolute value equations and inequalities in one variable.

A2.EI.1.a

Create an absolute value equation in one variable to model a contextual situation.
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A2.EI.1.b

Solve an absolute value equation in one variable algebraically and verify the solution graphically.
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A2.EI.1.c

Create an absolute value inequality in one variable to model a contextual situation.
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A2.EI.1.d

Solve an absolute value inequality in one variable and represent the solution set using set notation, interval notation, and using a number line.

A2.EI.1.e

Verify possible solution(s) to absolute value equations and inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.
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A2.EI.2

The student will represent, solve, and interpret the solution to quadratic equations in one variable over the set of complex numbers and solve quadratic inequalities in one variable.

A2.EI.2.a

Create a quadratic equation or inequality in one variable to model a contextual situation.

A2.EI.2.b

Solve a quadratic equation in one variable over the set of complex numbers algebraically.

A2.EI.2.c

Determine the solution to a quadratic inequality in one variable over the set of real numbers algebraically.
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A2.EI.2.d

Verify possible solution(s) to quadratic equations or inequalities in one variable algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.

A2.EI.3

The student will solve a system of equations in two variables containing a quadratic expression.

A2.EI.3.a

Create a linear-quadratic or quadratic-quadratic system of equations to model a contextual situation.
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A2.EI.3.b

Determine the number of solutions to a linear-quadratic and quadratic-quadratic system of equations in two variables.

A2.EI.3.c

Solve a linear-quadratic and quadratic-quadratic system of equations algebraically and graphically, including situations in context.

A2.EI.3.d

Verify possible solution(s) to linear-quadratic or quadratic-quadratic system of equations algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.
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A2.EI.4

The student will represent, solve, and interpret the solution to an equation containing rational algebraic expressions.

A2.EI.4.a

Create an equation containing a rational expression to model a contextual situation.
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A2.EI.4.b

Solve rational equations with real solutions containing factorable algebraic expressions algebraically and graphically. Algebraic expressions should be limited to linear and quadratic expressions.

A2.EI.4.c

Verify possible solution(s) to rational equations algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.

A2.EI.4.d

Justify why a possible solution to an equation containing a rational expression might be extraneous.

A2.EI.5

The student will represent, solve, and interpret the solution to an equation containing a radical expression.

A2.EI.5.a

Solve an equation containing no more than one radical expression algebraically and graphically.

A2.EI.5.b

Verify possible solution(s) to radical equations algebraically, graphically, and with technology, to justify the reasonableness of answer(s). Explain the solution method and interpret solutions for problems given in context.
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A2.EI.5.c

Justify why a possible solution to an equation with a square root might be extraneous.

A2.EI.6

The student will represent, solve, and interpret the solution to a polynomial equation.

A2.EI.6.a

Determine a factored form of a polynomial equation, of degree three or higher, given its zeros or the 𝑥-intercepts of the graph of its related function.

A2.EI.6.b

Determine the number and type of solutions (real or imaginary) of a polynomial equation of degree three or higher.
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A2.EI.6.c

Solve a polynomial equation over the set of complex numbers.

A2.EI.6.d

Verify possible solution(s) to polynomial equations of degree three or higher algebraically, graphically, and with technology to justify the reasonableness of answer(s). Explain the solution method and interpret solutions in context.
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