94 | eUreka Math algebra I StUdy gUIde
Lesson 21: Transformations of the Quadratic Parent Function, fx()=x^2
● (^) Students make a connection between the symbolic and graphic forms of quadratic
equations in the completed-square (vertex) form. They efficiently sketch a graph of a
quadratic function in the form fx()=-ax()hk^2 + by transforming the quadratic parent
function, fx()=x^2 , without the use of technology. They then write a function defined
by a quadratic graph by transforming the quadratic parent function.
Lesson 22: Comparing Quadratic, Square Root, and Cube Root Functions Represented in
Different Ways
● (^) Students compare two different quadratic, square root, or cube root functions
represented as graphs, tables, or equations. They interpret, contextualize, and abstract
various scenarios to complete the comparative analysis.
Lesson 23: Modeling with Quadratic Functions
● (^) 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.
Lesson 24: Modeling with Quadratic Functions
● (^) 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 the graph.
Module 5: a synthesis oF Modeling with eQuations
and Functions
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Students are introduced to functions for the first time in Grade 8, where they construct a
function that models a linear relationship between two quantities (8.F.B.4) and describe
qualitatively the functional relationship between two quantities by analyzing a graph (8.F.B.5).
In the first four modules of Algebra I, students learned to create and apply linear, quadratic,
and exponential functions in addition to square and cube root functions (F-IF.C.7). In Module
5, they synthesize what they have learned during the year by selecting the correct function
type in a series of modeling problems, without the benefit of a module or lesson title that
includes function type to guide them in their choices. This supports the standards’
requirement that students use the modeling cycle, at the beginning of which they must
formulate a strategy. Skills and knowledge from the previous modules support the
requirements of this module, including writing, rewriting, comparing, and graphing functions
(F-IF.C.7, F-IF.C.8, F-IF.C.9) and interpretation of the parameters of an equation (F-LE.B.5).
Students also draw on their study of statistics in Module 2, using graphs and functions to
model a context presented with data and tables of values (S-ID.B.6). In this module, we use
the modeling cycle rather than function type as the organizing structure.