11 Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Browse Components
Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### The degree of a polynomial function determines its behaviors and properties.

1 week

Evidence of Understanding

• describe connections between a polynomial equation and the features of its graph
• correlate the equation’s degree to the maximum number of real roots and end behavior
• distinguish a minimum or maximum point as absolute or relative using a function’s degree
• generalize how the equation’s lead coefficient impacts the graph’s direction and rate of change
• classify a function as odd, even or neither from both the equation and its graph
• analyze examples and nonexamples including polynomial, absolute value, trigonometric, rational, exponential, logarithmic, and radical functions
• describe how the graphs of even or odd functions reflect in the coordinate plane
• explain why the equation for an odd function cannot have a constant term

• investigate and and determine specific features of a parabola and its quadratic equation
• study various forms of a quadratic equations (factored, standard, vertex) to understand why a quadratic function has at most two real zeros
• possible extension: show how the degree limits a quadratic to at most 2 real zeros
• explore how the axis of symmetry relates to roots, the vertex, and other points on the parabola
• justify why the vertex always lies on the axis of symmetry
• use the axis of symmetry to explain why the vertex is located in the middle of the roots, and is the only point with an unrepeated output value
• approximate the roots of a given parabola and verify them using its quadratic equation
• use the degree to classify roots as real or imaginary
• connect characteristics of the roots with characteristics of the quadratic equation
• predict and justify the end behavior of a quadratic equation using its degree and lead coefficient

Develop conceptual understanding:

polynomial, degree, roots, zeros, absolute, relative, odd, even, quadratic, cubic, quartic, axis of symmetry, vertex

Supporting terms to communicate:

lead coefficient, exponent, reflect, minimum, maximum, end behavior, vertex form, standard form, factored form

Core Resource
A core resource supports multiple days of instruction.
• Distinguishing Functions: Even, Odd, Neither
This single-day resource supports students in identifying even and odd functions in both table and graph form and come up with their own definition.
Resource:
Distinguishing Functions: Even, Odd, Neither

Students will look at examples of Even and Odd functions to generate their own definitions and then further refine their definitions and understanding with a matching activity. There will also be opportunity for students to re-visit and refine their understanding of different function families.

All Resources From:
• Unit 4

#### Rational and Polynomial Functions

Instructional Routine: Connecting Representations
These tasks are embedded within the instructional routine called Connecting Representations.
• Parabola Features and Number of Real Roots
Students will be able to determine the number of real roots a quadratic has from its parabola features (e.g. axis of symmetry, vertex, etc.).
Resource:
Parabola Features and Number of Real Roots

Students will be able to determine the number of real roots a quadratic has from its parabola features (e.g. axis of symmetry, vertex, etc.).

All Resources From:
• Unit 4