Students compare the rate of change for simple and compound interest and recognize situations in which a quantity grows by a constant percent rate per unit interval.

Students describe and analyze exponential decay models; they recognize that in a formula that models exponential decay, the growth factor b is less than 1; or, equivalently, when b is greater than 1, exponential formulas with negative exponents could also be used to model decay.

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 and understand that if f is a function and x is an element of its domain, then f(x) denotes the output of corresponding to the input x.
Students use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Students understand set builder notation for the graph of a real-valued function: {(x, f(x)) | x ∈ D}.
Students learn techniques for graphing functions and relate the domain of a function to its graph.

Students understand the meaning of the graph of y = f(x), namely {(x,y) | x ∈ D and y = f(x)}.
Students understand the definitions of when a function is increasing or decreasing.

Students create tables and graphs of functions and interpret key features including intercepts, increasing and decreasing intervals, and positive and negative intervals.

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 functions that represent a geometric situation and relate the domain of a function to its graph and to the relationship it describes.

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.