Algebra 2, Chapter 5 Review

Transcription

1 Name: Class: Date: Algebra 2, Chapter 5 Review 4.4.1: I can factor a quadratic expression using various methods and support my decision. 1. (1 point) x x (1 point) x 2 x (1 point) 5x 2 22x : I can find the zeros (solutions, x-intercepts) of a quadratic function by factoring, using a table, using the quadratic formula or by graphing. 4. (1 point) 3x x + 42 = 0 5. (1 point) 2x 2 5x + 5 = 0 6. (1 point) x x = : I can accurately name a polynomial by its degree and number of terms. 7. (1 point) Classify 5x 4 + 6x 3 + 9x 2 by number of terms. 8. (1 point) Classify 3x 5 + 8x 3 8x by degree. 9. (1 point) Classify 2x 4 + 3x 2 by degree and by number of terms. 10. (2 points) Classify 7x 4 + 9x 3 + 6x 2 by degree and by number of terms. 11. (2 points) P1: Write x 2 ( 2x 2 + 3x 3 ) in standard form. Then classify it by degree and number of terms : I can identify the anatomy of a polynomial, including: leading coefficient, domain, range, end behavior, relative minima/maxima and graph polynomial functions. 12. (1 point) Use a graphing calculator to find the relative minimum, relative maximum, and zeros of y = 3x x 2 12x 60. If necessary, round to the nearest hundredth. 13. (1 point) What is the end behavior and maximum number of turning points for the equation Y = 4x 3 1x

2 Name: 14. (2 points) What is the relative Max and Min of the equation f(x) = x 3 + 2x 2 18x 15. (1 point) What is the end behavior and maximum number of turning points for the equation y = x 4 + 3x 3 2x (2 points) Find the zeros for the function y = (x + 3)(x 1)(x 2). Then Graph. Remember to use your knowledge about endbehavior, and to sketch the points between your zeros : I can factor a polynomial into its linear factors using GCF, trail and error, and formulas. 17. (2 points) 5x 3 55x x 18. (2 points) x 3 + 9x x 5.2.2: I can use a polynomial s factors to find its zeros and determine multiplicity. 19. (1 point) Find the zeros of f(x) = (x 4) 5 (x + 2) 5 and state the multiplicity. 20. (1 point) Find the zeros and state the multiplicity of hte equation f(x) = x 4 6x 3 + 8x : I can use zeros to construct teh equation of a polnomial in factored form and/or standard form. 21. (3 points) Write a polynomial function in standard form with zeros at 5, 4, and (1 point) What is a quartic polynomial function in standard form with zeros 2, -1, -3, and 1? 2

3 Name: 5.3.1: I can solve a polynomial using a variety of techniques and defend my choice. 23. (1 point) The dimensions in inches of a shipping box at We Ship 4 You can be expressed as width x, length x + 5, and height 3x 1. The volume is about 7.6 ft 3. Find the dimensions of the box in inches. Round to the nearest inch. 24. (1 point) Find the solutions of 19x 3 15x = x (1 point) Find the solutions of 19x 3 12x x = (1 point) Find the solutions of x 4 20x 2 = 64 a. 4, 4, 2, 2 b. 4, 2 c. 4, 4 d. no solution 5.4.1: I can divide polynomials (to help factor). 27. (2 points) Divide 3x 3 2x 2 4x 2 by x (2 points) Divide using synthetic division 8x 3 23x 2 4x 21 by (x + 3). 29. (2 points) Is (x + 5) a factor of P(x) = 3x x 2 9x 20? If it is, write P(x) as a product of two factors. a. yes: P(x) = (x + 5)(3x 2 x 4) c. yes: P(x) = (x 5)(3x 2 x 4) b. yes: P(x) = (x + 5)(3x 2 + x 4) d. (x + 5) is not a factor of P(x) 30. (1 point) Use synthetic division to find P( 2) for P(x) = x 4 + 3x 3 2x 2 2x : I can identify the number of roots of a polynomial using various techniques. 31. (1 point) How many real roots and complex roots does the following polynomial have? Give a value for the real root. y = 3x 4 2x (1 point) How many real roots and complex roots does the following polynomial have? Give a value for the real root. f(x) = x 4 + x 3 7x 2 9x (1 point) How many real roots and complex roots does the following polynomial have? Give a value for the real root. y = x 5 x 4 3x 3 4x + 4 3

4 Name: OA.5: I can identify the translation, the compression and the reflection of a polynomial function using graph translation theorem. 34. (1 point) What is the equation of y = x 3 under the following translations? horizontal translation right 3 units and vertical translation up 6 units 35. (1 point) vertical stretch by a factor of 3, horizontal shift 6 units to the right, vertical shift 6 units down 36. (2 points) What is the equation of y = x 3 under the following translations? vertical compression by a factor of 1, horizontal shift 4 units to the left, reflection across the x-axis : I can identify the best model to describe real life data and use the model to make predictions. 37. (1 point) What polynomial has a graph that passes through the given points? ( 4, 90), ( 1, 6), (1,0), (2,6) 38. (6 points) The table shows the amount of milk that Wisconsin dairy farms produced from 1937 to Year Milk Produced (in billions of lbs.) a.) What linear model fits the data best? b.) Use the linear model to estimate milk production in 1994? c.) What quadratic model fits the data best? d.) Use the quadratic model to estimate milk production in 1994? e.) Explain which model is best to use and why. 4

5 Algebra 2, Chapter 5 Review Answer Section 1. (x + 6)(x + 8) 2. (x 6)(x + 7) 3. (5x + 3)(x 5) 4. 6, ± , 7 7. trinomial 8. quintic 9. quintic trinomial 10. quartic trinomial 11. 3x 5 2x 4 ; quintic binomial 12. relative minimum: (0.36, 62.24), relative maximum: ( 3.69, 37.79), zeros: x = 5, 2, down/up 2 turning points 14. The relative maximum is at ( 3, 41) and the relative minimum is at (2, 22). 15. down down 3 turning points 16. l 17. 5x(x 6)(x 5) 18. x(x + 5)(x + 4) 19. 4, multiplicity 5; 2, multiplicity d 21. f(x) = x 3 7x 2 + 2x in. by 20 in. by 44 in. 1

6 24. 0, 0.92, , 1.29, A 27. 3x 2 8x + 12, R x 2 + x A f 32. f 33. f 34. y = (x 3) y = 3(x 6) y = 1 3 (x + 4) y = x 3 x 2 + 2x y = 0.039x