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Common Core: Math
CCLS  Math: G.GPE.3
 Category
 Expressing Geometric Properties With Equations
 SubCategory
 Translate Between The Geometric Description And The Equation For A Conic Section
 State Standard:
 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
5 Results

 Student Outcomes Students learn to graph equations of the form x2/a2  y2/b2 =1 . Students derive the equations of hyperbolas given the foci, using the fact that the difference of distances from the...

 Student Outcomes Students derive the equations of ellipses given the foci, using the fact that the sum of distances from the foci is constant.

 Student Outcomes Students convert between the real and complex forms of equations for ellipses. Students write equations of ellipses and represent them graphically.

 Topic A brings students back to the study of complex roots of polynomial functions. Students briefly review quadratic and cubic functions and then extend familiar polynomial identities to both...

 Students revisit the fundamental theorem of algebra as they explore complex roots of polynomial functions. They use polynomial identities, the binomial theorem, and Pascal’s Triangle to find roots...