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Volume 1, Issue 1 Math II Unit 1 Quadratic Functions Dear Parents, Welcome to the new school year! We are eager to work with you and your student as we learn new mathematical concepts. The State of Georgia is introducing Performance Standards that call for students to be actively engaged in doing math in order to learn math. In the classroom, students will frequently work on tasks and activities to discover and apply mathematical thinking. Students will be expected to explain or justify their answers and to write clearly and properly. Mathematical content will be organized in units based on the content of the Georgia Performance Standards (GPS). Since most textbooks published before the adoption of the new standards do not contain all the topics addressed in the new GPS, the teacher will be providing material in the form of a bound unit which contains graphic organizers for notes in class and supplementing practice through tasks. Below is information regarding Unit 1, Quadratic Functions. Look for future newsletters. Quadratic Functions – Georgia Performance Standards Students will represent & operate with complex numbers. Compute & simplify expressions with complex numbers Write square roots of negative numbers in imaginary form & complex numbers in the form of a + bi Students will analyze quadratic functions in the forms f(x) = ax² + bx + c and f(x) = a(x – h)² + k. Convert between standard and vertex form Graph quadratic functions as transformations of f(x) = x² Investigate & explain characteristics of quadratic functions Explore arithmetic sequences and compute their sums and partial sums Students will solve quadratic equations and inequalities in one variable. Solve equations graphically & with technology Find real & complex solutions of equations by factoring, taking square roots, and applying the quadratic formula Analyze roots using technology and the discriminate Solve quadratic inequalities both graphically and algebraically Describe the solutions using linear inequalities Textbook Connections Web Resources http://www.purplemath.com/modules/quadform.htm Mathematics II Text: (quadratic equation) Unit 1: Lessons 1-4 http://www.purplemath.com/modules/solvquad.htm (solving Unit 3: Lessons 1-2, 4-9 quadratic equations) Unit 4: Lessons 7-8 http://www.purplemath.com/modules/complex.htm (complex numbers) www.classzone.com http://www.wtamu.edu/academic/anns/mps/math/mathlab/col _algebra/col_alg_tut12_complexnum.htm (complex numbers) http://www.purplemath.com/modules/grphquad2.htm (vertex form) http://www.analyzemath.com/quadratics/quadratics.htm (standard form) http://www.purplemath.com/modules/ineqquad.htm (quadratic inequalities) http://www.regentsprep.org/Regents/math/algtrig/ATP2/Ari thSeq.htm (arithmetic sequences) http://www.regentsprep.org/Regents/math/algtrig/ATP2/Ari thSeq.htm (partial sums) Quadratic Function Vocabulary Terms Horizontal Shift: transformation of a graph left or right Complete factorization over the integers: writing a polynomial as a product of polynomials as that none of the factors is the number 1, there is at most one factor of degree zero, each polynomial factor has degree less than or equal to the degree of the product polynomial, each polynomial factor has all integer coefficients, and none of the factor polynomial can be written as such a product. Vertex Form: a formula f(x) = a(x-h)²+k, where a is a nonzero constant and the vertex of the graph is the point (h,k) Discriminate: in the quadratic equation, the value of b²-4ac Theorems: 1) The graph of any quadratic function can be obtained from transformations of the graph of f(x) = x² 2) The discriminate is positive, zero, or negative if & only if the equation has 2 real solutions, 1 real solution or 2 complex conjugate solutions respectively b b2 4ac 3) Quadratic Formula: x 2a b 4) For h and k f( b ) , f(x) = a(x-h)²+ k is the same function as f(x) = ax²+ bx + c 2a 2a For examples & help with vocabulary, visit: http://intermath.coe.uga.edu/ Practice 1. What happens to the graph of y = x² when you multiply x² by 3? 2. Find the product of (2x + 3) (3x + 4). 3. Factor 6x² +7x -20. 4. Solve the quadratic equation: 2x² + 3x – 54 = 0. 5. Find the y-intercept of f(x) = x²- 4x + 9. 6. Find the discriminate of 3x² +15x = 12 7. Write an expression for 81 . Answers: 1. It causes a vertical stretch: 2. (6x²+17x+12) 3. (2x+5)(3x -4) 4. (2x-9)(x+6)=0 x = 4.5 or x = -6 5. f(0) = 0²-4(0) +9 y-intercept=9 6. b²-4ac = (15)²-4(-36) = 369 7. -9i

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posted: | 8/16/2011 |

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