redch0 - Contents 0 REVIEW NOTES 1 0.0 Quadratic Equations...

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Unformatted text preview: Contents 0 REVIEW NOTES 1 0.0 Quadratic Equations and Completing the Square . . . . . . . . . . . . . . . . . . . . . . . . . 1 0.1 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 0.2 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 0.3 Absolute Values and Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 0.4 Quadratic Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 0.5 The Chart Method for Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 0.6 Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 0.7 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 0.7.1 Radian Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 0.7.2 Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 0.7.3 Trigonometric Identities and Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 0.7.4 Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 0.8 Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2 CONTENTS Chapter 0 REVIEW NOTES 0.0 Quadratic Equations and Completing the Square Factor the following quadratic expressions 1. x 2- 3 x , 2 x 2 + x , πx 2 + 3 π , 17 x 2 + 51 x and √ 2 x 2 + 2 x 2. x 2- 9 and x 2- 49 3. x 2- 3 and x 2- 1 4. x 2- 2 and x 2- π 5. x 2 + x + 1 / 4 and x 2 + x + 6 6. x 2- x + 1 / 4 and x 2- x- 6 7. x 2 + 2 a + a 2 and x 2 + ( a + b ) x + ab 8. x 2- 2 x + 3 and x 2- 3 x- 40 9. 3 x 2- 5 x- 2 and 8 x 2 + 2 x- 1 10. 2 x 2- 5 bx- 3 b 2 and x 2- 4 x- 21 11. x 4- 2 x 2 + 1 and x 6- 4 x 3- 21 Solve the following equations by completing the square 12. 3 x 2 + 6 x- 1 = 0 13. 3 x (3 x- 2) = 6 x- 5 14. y 2- 15 y- 4 = 0 15. 6 u 2 + 7 u- 3 = 0 16. x 2- 2 x + 9 = 0 17. 4 z 2- 4 z- 1 = 0 18. p (2 p- 4) = 5 19. ( x- 2) 2 + 3 x- 5 = 0 20. (3 x- 2) 2 + ( x + 1) 2- 21. 5 y 2- 15 y + 9 = 0 Use the quadratic formula to solve the following equations 22. 5 x 2 + 6 x- 1 = 0 23. 2 x 2 = 18 x + 5 24. x (2 x- 3) = 2 x- 6 25. 6 x 2- 7 x + 2 = 0 26. 2 x 2 = 13( x- 1) + 3 27. 2 x 2- 6 x- 1 = 0 28. 1200 y 2 = 10 y + 1 29. x 2 + 2 bx- c 2 = 0 30. x 2- 6 ax + 3 a 2 = 0 31. πu 2 + ( π 2- 1) u- π = 0 32. x ( x- √ 2 + 4) = 4( x + 1) 33. 3 x 2 = 5( x- 1) 2 2 REVIEW NOTES For the following functions f find the discriminant of f ( x ) = 0 and determine whether the roots are real and unequal, real and equal, or do not exist. Graph f ( x ) without plotting more than four points....
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redch0 - Contents 0 REVIEW NOTES 1 0.0 Quadratic Equations...

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