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Use the structure of the quadratic form of the quartic function to factor into two difference of squares.

Chunk a diagram, change the form of the diagram to add a right triangle, connect to what students know about the Pythagorean theorem to connect to derivations of the equation of a parabola.

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.

After this unit, how prepared are your students for the end-of-course Regents examination?  The end of unit assessment is designed to surface how students understand the mathematics in the unit.  It includes spiralled multiple choice and constructed response questions, comparable to those on the end-of-course Regents examination.  A rich task, that allows for multiple entry points and authentic assessment of student learning, may be available for some units and can be included as part of the end of unit assessment.  All elements of the end of unit assessment are aligned to the NYS Mathematics Learning Standards and PARCC Model Frameworks prioritization.  

Students will have opportunity to identify and use different properties including difference of squares and square of a sum as well as see relationship to applying understanding of quadratics to higher degree polynomials.

This applet allows you to support students in exploring the relationship between the real and complex roots of a pair of quadratic functions that are mirror images of each other.

Use the structure of a set of graphed and factored polynomials to make connections between the two.

To use the structure of a quadratic equation to find shortcuts for solving quadratic equations.

Students will be given function formula and unlabelled graph of quartic function in quadratic form. It is also an even function. Students must find two of the points (whichever they want).

To use the structure of a polynomial given in factored form to find the y-intercept of the function.

Students can use different strategies to predict how many real solutions a quadratic function written in vertex form has.

To use the structure of a quadratic equation to find shortcuts for solving quadratic equations.