Solve+Systems+of+Linear+and+Quadratic+Equations+(Cedar+City,+UT,+refers+to+A.REI.7)

Systems of Linear and Quadratic Equations SWBAT: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
 * __Unit Goal__**

**b.** solve a simples system consisting of a linear equation and a quadratic equation in two variables algebraically.
 * __Content Standards__**
 * A.REI.7 Solve systems of equations **
 * a. ** solve a simples system consisting of a linear equation and a quadratic equation in two variables graphically.


 * __Integrate the Practice Standards throughout the learning cycles:__**

1) Know that a quadratic function is a vertical parabola and a quadratic equation can be a parabola or any conic section. 2) Understand what a system is 3) Understand the nature of solutions 4) Solve systems 5) Understand quadratic functions, unit circle and linear functions

Launch: Given various graphs of linear functions graphed with quadratic functions, identify solutions (points of intersection) and recognize how many solutions are possible for each system shown. Examples: []
 * __Develop:__**
 * __Activity 1:__**
 * __See also:__**

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__**Discuss:**__ Bring class back together to share how many solutions are shown and what the solutions are.
 * __Explore:__** Have students discuss and identify points of intersection (solutions to the systems) and determine how many solutions.

Activity 2 : Launch: See You Later Alligator
 * __Solidify__**

Explore: Have students graph the functions and also solve the systems of equations algebraically. What do the graphs and points of intersection on the graphs represent? Discuss: Bring class back together and discuss questions #2, #3.

Activity 3: Launch: The price C, in dollars per share, of a high-tech stock has fluctuated over a twelve-year period according to the equation C =14 +12x - x2, where x is in years. The price C, in dollars per share, of a second high-tech stock has shown a steady increase during the same time period according to the relationship C = 2x + 30.
 * __Practice__**

Explore: (a) Will the values ever be the same? If so, when? (b) Determine the values of // x // for which the quadratic stock price is greater than the linear stock price. Discuss: Was it easier/harder to find solutions graphically or algebraically? Which method is the most accurate?