Algebra 2 Unit 2: Quadratics

Unit Driving Question 

Where are quadratic functions used in the world?

Essential Questions 

1. What are the distinguishing characteristics of a quadratic?

2. How can we identify key features of a quadratic?

3. What mathematical and real-world value do quadratic functions possess?

4. How are quadratic functions used to solve real-world problems?

5. How are complex numbers related to real numbers? 

Launch Task 

Big Ideas for Development Lessons 

Closure & Assessment 

1 Lesson 

4 Weeks (approximately 1 week per big idea) 

1 Week 

Option 1: Instructions and activity for Unit 1 Hook: Fall of Javert

Click on the links below to see each Big Idea's Lesson Overview (includes links to teacher notes and student activities) 

1. A quadratic function has degree 2. 
2. The graph and equation of a quadratic function can yield information about its roots. (*8-10 days)
3. Equivalent representations of a function highlight different properties. 

1. Formative Assessment after Big Idea 2: Solving Quadratics Maze or Parabola Slolam
2. Re-engagement Activity (not provided)
3. Unit 2 Assessment:  Summative Assessment

Big Idea 1: A quadratic function has degree 2.

Lesson Plans

• Big Idea 1 Lessons 1-3 Overview (includes links to teacher notes and student activities)
• Quadratics Unit/Lesson Progression (New Visions for Public Schools) 

Additional Activities

• Quadratics- RetroDesmos Collection These Desmos activities connect classic video games with mathematics concepts.
• Fall of Javert (Mathalicious) At the end of the popular musical Les Misérables, Inspector Javert falls from a bridge in the middle of Paris into the river below. As he falls, he sings...and sings...and sings. In this lesson, students use quadratic functions to explore the mathematics of how objects fall. How high was Javert’s bridge, how fast was he traveling when he hit the water, and what’s the maximum height from which someone can safely jump?

Evidence of Understanding 

Discover and describe the characteristics of a quadratic function in mathematical and real world situations.

• Using various tools including technology, generalize the difference between quadratic functions and other functions.

• Use graphs, tables, and equations with the aide of technology to allow students to grapple with the differences and similarities between quadratics and linear functions, including targeting rates of change.

• Create a quadratic equation given a graph, or table of values.

Identify critical points and key features of the graph of a quadratic function and interpret meanings in mathematical and real world situations.

• Identify the following features from the table or graph of a quadratic function using words, algebraic symbols, equations and inequalities, interval notation: intercepts, symmetry, maximum and minimum points, intervals of increase and decrease, intervals of positive and negative values, domain and range.

• Describe critical points and key features in the correct context of a mathematical and real world situation.

Make generalizations about how transformations affect key features of the graph of a quadratic function.

• Form conjectures about the effects each transformation will have on critical points and key features.

• Use graphs, tables and various tools to justify the conclusions.

Big Idea 2: The graph and equation of a quadratic function can yield information about its roots.

Lesson Plans

Big Idea 2 Lessons 1-3 Overview (includes links to teacher notes and student activities)

Additional Activities

Quadratics- RetroDesmos Collection These Desmos activities connect classic video games with mathematics concepts.

Evidence of Understanding 

Determine rational roots of a factorable quadratic function.

• Explore and conjecture about the characteristics of a factorable and non-factorable quadratic equation. Use technology to verify.

• Factor quadratic functions in various forms. Confirm solutions with the graph of the quadratic function.

• Recognize the connection between the factors of a quadratic function and the roots and zeros of the graph of a quadratic function.

• Describe the connection between the quadratic equation (factors and roots) and the graph of the quadratic function (x-intercepts).

• Solve by factoring quadratic equations in various forms.

• Make a connection between the solutions of the equation to characteristics on the table or graph of the function using technology (i.e. graphing calculators, Desmos,etc.).

• Recognize special factorable quadratic equations: perfect square trinomials and the difference of two squares.

• Explore the relationship between quadratics that are perfect square trinomials, difference of two squares, factorable with rational roots, factorable with non-rational roots and the graphs of each function. Use technology to test the findings.

• Solve quadratic equations in various forms.

• Make a connection between the solutions of the equation to characteristics on the table or graph of the function using technology (i.e. graphing calculators, Desmos,etc.).

• Notice situations where roots will be irrational, imaginary or complex roots. Generalize and justify your findings.

• Accept or reject findings based on the mathematical or real world situation.

• Recognize possible solutions to a quadratic function from a table, graph, and equation.

• Create a possible graph or equation for a quadratic function from given solutions and characteristics.

Describe various types of solutions to a quadratic equation.

• Form conjectures about the roots of a quadratic equation by looking at the graph or table.

• Calculate and identify roots as imaginary, rational, irrational or complex using various techniques to solve quadratic equations.

• Determine the best method for finding roots (ie completing the square, quadratic formula, factoring, graphing, etc).

• Discover how the quadratic formula and completing the square of a quadratic equation are related.

Conjecture and form generalizations about the graph of a quadratic function based on its roots and characteristics and vice versa.

• Discover how the type of roots, the discriminant, the equation and the graph of a quadratic equation are related.

• Create a visual model of a quadratic function given an equation. Identify the  components of the equation and graph.

• Explore how real world situations can be modeled by quadratic functions and identify the relevance of roots and the characteristics of the graph. 

Big Idea 3: Equivalent representation of function highlights different properties.

Lessons and Additional Activities

• Big Idea 3 Lessons 1-2 Overview (includes links to teacher notes and student activities)

Additional Assessment

• Launching Water Balloons Performance Assessment (covers A2.A.1.1, A2.A.2.3, A2.F.1.1, A2.F.1.2, A2.F.1.3)- For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module.    

Evidence of Understanding 

Identify and verify equivalent representations for various forms of quadratic functions.

• Recognize important characteristics of a quadratic function when given in various forms ie. factored, standard, and vertex form.

• State the advantages of using each form.

• Build a quadratic equation from a graph or table.

• Connect multiple representations of a quadratic function by identifying special characteristics and critical points.

• Relate real world scenarios to the appropriate representation of a quadratic function.

• Develop real world scenarios to match the various representations. Identify and justify the relevance of the characteristics and critical points on the quadratic function.