Section	Teacher-facing learning goals
A Different Kind of Change	Lesson 1 Describe (orally and in writing) a relationship that increases then decreases when represented by a graph. Given an interesting context, create drawings, tables, and graphs that represent a quadratic relationship. Lesson 2 Comprehend that a “quadratic relationship” can be expressed with a squared term. Describe (orally and in writing) a pattern of change associated with a quadratic relationship. Determine and explain (orally and in writing) whether a visual pattern represents a linear, exponential, or quadratic relationship.
Quadratic Functions	Lesson 3 Comprehend that the same quadratic function can be expressed symbolically in different ways. Interpret (using words and other representations) the quadratic relationships in growing patterns as functions, where each input gives a particular output. Write expressions that define quadratic functions. Lesson 4 Use graphs, tables, and calculations to show that exponential functions eventually overtake quadratic functions. Lesson 5 Explain (orally and in writing) the meaning of each term in a quadratic expression that represents the height of a free-falling object. Use tables, graphs, and equations to represent the height of a free-falling object. Write quadratic functions to represent the height of an object falling due to gravity. Lesson 6 Create graphs of quadratic functions that represent a physical phenomenon and determine an appropriate domain when graphing. Identify and interpret (orally and in writing) the meaning of the vertex of a graph and the zeros of a function represented in tables and graphs. Write and interpret (orally and in writing) quadratic functions that represent a physical phenomenon. Lesson 7 Choose an appropriate domain for a quadratic function representing a context and explain (orally) the reasoning why it was selected. Interpret (orally and in writing) the vertex of a graph and the zeros of a quadratic function in context. Write and graph equations to model economic situations characterized by quadratic functions.
Working with Quadratic Expressions	Lesson 8 Use area diagrams to reason about the product of two sums and to write equivalent expressions. Use the distributive property to write equivalent quadratic expressions. Lesson 9 Comprehend the terms “standard form” and “factored form” (in written and spoken language). Use rectangular diagrams to reason about the product of two differences or of a sum and difference and to write equivalent expressions. Use the distributive property to write quadratic expressions given in factored form in standard form. Lesson 10 Coordinate (orally and in writing) a quadratic expression given in factored form and the intercepts of its graph. Interpret (orally and in writing) the meaning of \(x\)-intercepts and \(y\)-intercepts on a graph of a quadratic function that represents a context.
Features of Graphs of Quadratic Functions	Lesson 11 Create graphs of quadratic functions that are in factored form. Given a quadratic function in factored form, explain how to determine the vertex and \(y\)-intercept of its graph. Lesson 12 Comprehend (orally and in writing) how the \(a\) and \(c\) in \(y=ax^2 + bx + c\) are visible on the graph. Coordinate (orally and in writing) different representations of quadratic functions (expressions, tables, and graphs). Use technology to explore how the parameters of quadratic expressions in standard form are visible on the graph. Lesson 13 - Optional Describe (orally and in writing) how the \(b\) in \(y=ax^2+bx+c\) affects the graph. Write quadratic expressions in standard and factored forms that match given graphs. Lesson 14 Interpret (orally and in writing) the graph and equation representing a function in terms of the context. Lesson 15 Comprehend quadratic expressions in “vertex form” by seeing the form as a constant plus a coefficient times a squared term. Coordinate (using words and other representations) the parameters of a quadratic expression in vertex form and the graph that represents it. Lesson 16 Create a graph of a quadratic function written in vertex form, showing a maximum or minimum and the \(y\)-intercept. Use an equation in vertex form to identify the maximum or minimum of a quadratic function. Lesson 17 Create a quadratic function by changing the vertex of an existing function given its equation, graph, and a description. Describe informally (orally and in writing) the effect on the graph of a quadratic function when performing simple algebraic transformations.

Alg1.6: Introduction to Quadratic Functions