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New York Math

Algebra II: Algebra - Reasoning with Equations and Inequalities

Understand solving equations as a process of reasoning and explain the reasoning.

AII-A.REI.1b

Partially covered
Explain each step when solving rational or radical equations as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
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AII-A.REI.2

Mostly covered
Solve rational and radical equations in one variable, identify extraneous solutions, and explain how they arise.

Solve equations and inequalities in one variable.

AII-A.REI.4

Solve quadratic equations in one variable.

AII-A.REI.4.b

Mostly covered
Solve quadratic equations by: i) inspection, ii) taking square roots, iii) factoring, iv) completing the square, v) the quadratic formula, and vi) graphing. Write complex solutions in a + bi form. (Shared standard with Algebra I)

AII-A.REI.7b

Fully covered
Solve a system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. (Shared standard with Algebra I)
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Represent and solve equations and inequalities graphically.

AII-A.REI.11

Mostly covered
Given the equations y = f(x) and y = g(x): i) recognize that each x-coordinate of the intersection(s) is the solution to the equation f(x) = g(x); ii) find the solutions approximately using technology to graph the functions or make tables of values; iii) find the solution of f(x) < g(x) or f(x) ≤ g(x) graphically; and iv) interpret the solution in context. (Shared standard with Algebra I)