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Educational Opportunity

This educational opportunity provides a guide to factoring quadratic expressions and solving quadratic equations. Learn how to find the zeroes of quadratic functions and solve matrix equations. Review the concepts of the vertex, axis of symmetry, and x-intercepts. Explore the determinant and factorization methods. Practice through examples and application problems in various scenarios.

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Educational Opportunity

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  1. Educational Opportunity • p. 260, #3, 23, 24, 37, 42, 51, 60, 63, 69, 74, 78, 80, 90, 92, 101, 110, 113 Honey’s Ready for some work…Are you??

  2. Chapter 5-2 Solving Quadratic Equations by Factoring Goals: Factor quadratic expressions and solve quadratic equations by factoring Find zeroes of quadratic functions

  3. Review Label the vertex, axis of symmetry, and x-intercepts Solve the matrix equation Write the linear system as a matrix equation

  4. Find the Determinant • [12 4 -1] • [-2 3 2] • [5 8 1]

  5. Guide to Factoring • Pull out Greatest Common Factor • Identify if the quadratic is a binomial or trinomial • If binomial it must be a DIFFERENCE OF SQUARES • If trinomial…

  6. Trinomials • Two types of trinomials • For type #1, find the factors of c that add up to b • Those factors (x + __)(x + __) go in blanks • For type #2, multiply a & c together. Find the factors of ac that add up to b. Then factor by grouping • Those blanks are the two factors found that add up to c. • Find the GCF of both parenthesis & rewrite with two ( )( )

  7. Factor, Factor, Factor

  8. Factoring with Zero Product Property Find the “zeroes” of a quadratic are the x-intercepts of the graph

  9. Intercept form & zeroes • Write the quadratic function in intercept form and give the function’s zeroes.

  10. Stained Glass • You have made a rectangular stained glass window that is 2 feet by 4 feet. You have 7 square feet of clear glass to create a border of uniform width around the window. What should the width of the border be?

  11. Great America • You own an amusement park that averages 75,000 visitors per year who each pay a $12 admission charge. You plan to lower the admission price to attract new customers. It has been shown that each $1 decrease in price results in 15,000 new visitors. What admission should you charge to maximize your annual revenue? What is the maximum revenue?

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