Algebra

Interpret expressions that represent a quantity in terms of its context.

Identify and interpret parts of a quadratic, square root, inverse variation, or right triangle trigonometric expression, including terms, factors, coefficients, radicands, and exponents.

Interpret quadratic and square root expressions made of multiple parts as a combination of single entities to give meaning in terms of a context.

Write an equivalent form of a quadratic expression by completing the square, where 𝑎 is an integer of a quadratic expression, 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, to reveal the maximum or minimum value of the function the expression defines.

Extend the understanding that operations with polynomials are comparable to operations with integers by adding, subtracting, and multiplying polynomials.

Create equations and inequalities in one variable that represent quadratic, square root, inverse variation, and right triangle trigonometric relationships and use them to solve problems.

Create and graph equations in two variables to represent quadratic, square root and inverse variation relationships between quantities.

Create systems of linear, quadratic, square root, and inverse variation equations to model situations in context.

Justify a chosen solution method and each step of the solving process for quadratic, square root and inverse variation equations using mathematical reasoning.

Solve and interpret one variable inverse variation and square root equations arising from a context, and explain how extraneous solutions may be produced.

Solve for all solutions of quadratic equations in one variable.

Understand that the quadratic formula is the generalization of solving 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 by using the process of completing the square.

Explain when quadratic equations will have non-real solutions and express complex solutions as 𝑎 ± 𝑏𝑖 for real numbers 𝑎 and 𝑏.

Use tables, graphs, and algebraic methods to approximate or find exact solutions of systems of linear and quadratic equations, and interpret the solutions in terms of a context.

Extend the understanding that the 𝑥-coordinates of the points where the graphs of two square root and/or inverse variation equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥) and approximate solutions using graphing technology or successive approximations with a table of values.