## Mathematics: Polynomials & Parabolas

This is the fourth semester of a two-year Algebra sequence and a PBAT class. The PBAT will reflect an in depth studies of parabolas, the main topic of this course. Parabolas occur frequently in the real world and have many applications in art, architecture, engineering, physics and technology. For example, because of their U-shape and reflective properties, parabolic solar panels are constructed to harness solar energy: as solar rays hit the panels they reflect to converge towards a central focus, where heat concentrates, and from which it is transferred to a power generator.

Learning Goals: We will first review how to factor polynomials and then work with rational expressions. Next we will investigate and graph linear equations: order pairs on a coordinate plane, relations vs functions, domain, range, slopes, x and y intercepts. We will wrap this unit by solving a system of equations in two variables. These same topics will be explored in quadratic functions.

Other main topics are: vertex, axis of symmetry, y-intercept and direction. To find the x-intercepts: factoring, using the quadratic formula, and completing the square. Standard and vertex forms of quadratic equations. How to write a quadratic function given the x-intercepts, vertex or three points of the equation. Real life application of quadratic equations: finding the maximum profit or minimum cost for a business. Finally we will explore the parabola as one of the conic sections: geometric definition, distance formula, focus, directrix, latus rectum and properties (angle reflections). How to write quadratic functions given some of the listed components.

Media Used:
http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/emat6690/Insunit/parabola/
http://tutorial.math.lamar.edu/Classes/Alg/Parabolas.aspx#Graph_Para_Ex1_a
http://www.cut-the-knot.org/ctk/Parabola.shtml
http://www.nrel.gov/csp/troughnet/solar_field.html
http://www.ucsusa.org/clean_energy/technology_and_impacts/energy_technologies/how-solar-energy-works.html
http://www.eere.energy.gov/de/csp.html
Significant Assignments:

Tests and quizzes. Work must be explained.

Sample PBATs:
“How the properties of parabolas are employed in producing solar energy”.
“What equations can be used for parabolic solar panels?"