Unit 7: Structures of Quadratic Expressions
This unit explores different forms of writing a quadratic function and how the different forms reveal features of the graph of a quadratic function. It discovers the process for completing the square on a quadratic function and connects it to graphing a parabola, using transformations. It also introduces factoring trinomials, multiplying binomials to move between factored and standard forms of quadratic equations, and using the factored form to find the x-intercepts of the graph. Graphs of quadratic functions and different forms of the equation of a quadratic function become the basis for solving quadratic equations. It connects the factors of a quadratic function to the x-intercepts of the graph and to the solution of the equation when f(x) = 0.
The unit begins by introducing transformations of quadratic functions and how to write equations for the graphs of quadratic functions in vertex form, given the graph of a function. Then it focuses on completing the square and on squaring binomials, using area models. Then connects how to graph a parabola in vertex form and how to complete the square. Next the unit focuses on factoring and multiplying binomials, relating the factored form of a function to its graph using area models to organize and justify thinking, and to notice patterns between a, b and c. Then it relates the factors of a quadratic function to the x-intercepts of the graph and develops a strategy for finding the vertex and line of symmetry using the x-intercepts as well as using different forms of quadratic functions to efficiently graph and write equations.
Finally, the unit connects the understanding of the graphs of quadratic functions to solving quadratic equations with real solutions, both graphically and algebraically; solving quadratic equations by factoring, completing the square, and using inverse operations. The quadratic formula is also used for equations with real solutions. The unit ends by developing fluency in solving quadratic equations by comparing the methods for different quadratic equations.
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Transcript
Unit 7: Structures of Quadratic Expressions
This unit explores different forms of writing a quadratic function and how the different forms reveal features of the graph of a quadratic function. It discovers the process for completing the square on a quadratic function and connects it to graphing a parabola, using transformations. It also introduces factoring trinomials, multiplying binomials to move between factored and standard forms of quadratic equations, and using the factored form to find the x-intercepts of the graph. Graphs of quadratic functions and different forms of the equation of a quadratic function become the basis for solving quadratic equations. It connects the factors of a quadratic function to the x-intercepts of the graph and to the solution of the equation when f(x) = 0. The unit begins by introducing transformations of quadratic functions and how to write equations for the graphs of quadratic functions in vertex form, given the graph of a function. Then it focuses on completing the square and on squaring binomials, using area models. Then connects how to graph a parabola in vertex form and how to complete the square. Next the unit focuses on factoring and multiplying binomials, relating the factored form of a function to its graph using area models to organize and justify thinking, and to notice patterns between a, b and c. Then it relates the factors of a quadratic function to the x-intercepts of the graph and develops a strategy for finding the vertex and line of symmetry using the x-intercepts as well as using different forms of quadratic functions to efficiently graph and write equations. Finally, the unit connects the understanding of the graphs of quadratic functions to solving quadratic equations with real solutions, both graphically and algebraically; solving quadratic equations by factoring, completing the square, and using inverse operations. The quadratic formula is also used for equations with real solutions. The unit ends by developing fluency in solving quadratic equations by comparing the methods for different quadratic equations.
Click Here
Digital Workbook
PDF Version (Printable)
Found Directly in Delta Math --> Examples --> Videos
Homework Hints
Help, Hints and Explanation Videos
Click Here
How to Set up Your Account
Key Lesson Takeaways