Students understand that a function from one set (called the domain) to another set (called the range) assigns each element of the domain to exactly one element of the range.
Students use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Students create models and understand the differences between linear and exponential models that are represented in different ways.

Students apply knowledge of exponential functions and transformations of functions to a contextual situation.

Students apply knowledge of exponential functions and transformations of functions to a contextual situation.

Students understand that factoring reverses the multiplication process as they find the linear factors of basic, factorable quadratic trinomials.
Students explore squaring a binomial, factoring the difference of squares, and finding the product of a sum and difference of the same two terms.

Students solve increasingly complex one-variable equations, some of which need algebraic manipulation, including factoring as a first step and using the zero product property.

Students rewrite quadratic expressions given in standard form, ax2 + bx + c (with a = 1), in the equivalent completed-square form, a(x - h)2 + k, and recognize cases for which factored or completed-square form is most efficient to use.

Students solve complex quadratic equations, including those with a leading coefficient other than 1, by completing the square. Some solutions may be irrational. Students draw conclusions about the properties of irrational numbers, including closure for the irrational number system under various operations.

Students derive the quadratic formula by completing the square for a general quadratic equation in standard form, ax2 + bx + c = 0, and use it to verify the solutions for equations from the previous lesson for which they have already factored or completed the square.

Students use the quadratic formula to solve quadratic equations that cannot be easily factored.
Students understand that the discriminant, b2 - 4ac, can be used to determine whether a quadratic equation has one, two, or no real solutions.

Students graph simple quadratic equations of the form y = a(x - h)2 + k (completed-square or vertex form), recognizing that (h,k) represents the vertex of the graph and use a graph to construct a quadratic equation in vertex form.
Students understand the relationship between the leading coefficient of a quadratic function and its concavity and slope and recognize that an infinite number of quadratic functions share the same vertex.

Students compare the basic quadratic (parent) function, y = x2, to the square root function and do the same with cubic and cube root functions. They then sketch graphs of square root and cube root functions, taking into consideration any constraints on the domain and range.

Students write the quadratic function described verbally in a given context. They graph, interpret, analyze, check results, draw conclusions, and apply key features of a quadratic function to real-life applications in business and physics.

Students create a quadratic function from a data set based on a contextual situation, sketch its graph, and interpret both the function and the graph in context. They answer questions and make predictions related to the data, the quadratic function, and graph.

From a graphic representation, students recognize the function type, interpret key features of the graph, and create an equation or table to use as a model of the context for functions addressed in previous modules (i.e., linear, exponential, quadratic, cubic, square root, cube root, absolute value, and other piecewise functions).

Students recognize linear, quadratic, and exponential functions when presented as a data set or sequence, and formulate a model based on the data.

Students create a two-variable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. They interpret the graph and function and answer questions related to the model, choosing an appropriate level of precision in reporting their results.

Students recognize when a table of values represents an arithmetic or geometric sequence. Patterns are present in tables of values. They choose and define the parameter values for a function that represents a sequence.

Students use linear, quadratic, and exponential functions to model data from tables, and choose the regression most appropriate to a given context. They use the correlation coefficient to determine the accuracy of a regression model and then interpret the function in context. They then make predictions based on their model, and use an appropriate level of precision for reporting results and solutions.

Using tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.