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Unit 3 Review for Common Assessment

Unit 3 Review for Common Assessment. Match the graph of a quadratic function with it’s equation below:. f(x ) = x 2. f(x ) = -(x+2) 2 +4. f(x ) = (x+2) 2 -1. Describe the end behavior of the graph of each given graph.

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Unit 3 Review for Common Assessment

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  1. Unit 3 Review for Common Assessment

  2. Match the graph of a quadratic function with it’s equation below: f(x) = x2 f(x) = -(x+2)2+4 f(x) = (x+2)2-1

  3. Describe the end behavior of the graph of each given graph.

  4. Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. 1.) f(x) = -x3 + 4x Rise Left, fall right EVEN 2.) f(x) = x4 – 5x2 +4 Rise left, rise right 3.) f(x) = x5 - x Fall left, rise right 4.) f(x) = x3 – x2 - 2x 5.) f(x) = -2x4 + 2x2 Fall left, rise right Fall left, fall right

  5. Determine without graphing, the critical points of each function. 1.) f(x) = (x + 2)2 - 3 2.) f(x) = -x2 + 6x - 8 f’(x) = -2x + 6 f’(x) = 2x + 4 Max (3,1) Min (-2,-3) 3.) f(x) = 3x3 - 9x + 5 4.) = x3 + 6x2 + 5x f’(x) = 9x2 - 9 Min (-.47, -1.13) Max (-3.53, 13.12) Pt. of Inflection (-2,6) f’’(x) = 18x Min ( 1, -1) Max (-1, 11) Pt. of Inflection ( 0 , 5) Min ( -√5, -16) Max (0, 9) Min ( √5 , -16) 5.) f(x) = x4 - 10x2 + 9

  6. Find the zeros of each polynomial function. 1.) x2 – 40 = 0 2.) x3 + 4x2 + 4x = 0 x = 0, -2, -2 4.) x2 + ¾x + ⅛ = 0 3.) x2 + 11x – 102 = 0 x = -17, 6 x = -½, -¼ If you can’t figure it out then use Quadratic Formula

  7. Find the zeros of the polynomial function by factoring. 1.) f(x) = x3 + 5x2 – 9x - 45 1.) f(x) = x3 + 4x2 – 25x - 100 x = 5, -5, -4

  8. Which of the following is a rational zero of f(x) = –2x5 + 6x4 + 10x3 – 6x2 – 9x + 4 1, -3, -2, 4, -1 ???? Remember you could use synthetic division or just do p(x) and see if you get a remainder of ZERO OR = 0 So 4 is a factor, the others are not

  9. Use synthetic division to divide x4 + x3 – 11x2 – 5x + 30 by x - 2 . Then divide by x + 3 Use the result to find all zeros of f(x). x2x C R So you are left with: x2 - 5 Then all the zeroes are: -3, , 2

  10. List all possible rational zeros of 1.) 2.)

  11. List all possible rational roots, use synthetic division to find an actual root, then use this root to solve the equation. f(x) = 2x4 + x3 – 31x2 – 26x + 24 Hint 4 and -3/2 are roots 2x2 + 6x – 4 USE QUADRATIC FORMULA!!!

  12. Find the number of possible positive, negative, and imaginary zeros of: P N I P N I 2,0 positive roots 1 positive root 2 0 0 0 0 2 1 1 3 1 0 2 0 negative roots 3,1 negative roots 3,1 positive roots P N I 3,1 positive roots P N I 2 0 2 0 0 2 2 4 3 3 1 1 3 1 0 2 1 1 1 positive root 2,0 positive roots

  13. Use the given root to find the solution set of the polynomial equation. p(x) = x4 + x3 – 7x2 – x + 6 GIVEN -3 IS A ROOT Then we can find the rest by factoring: So the roots are: -3, -1, 1, and 2

  14. Which equation represents the graph of the function? f(x) = 2x2+2x-1 f(x) = -x2-3x+4 f(x) = x2+10x-1

  15. Approximate the real zeros of each function. -2.5 0.7, -0.7 2.3 -0.4 and -2.6

  16. Use the given root to find the solution set of the polynomial equations 2i 3-i Since 3-i is a root, so is 3+i Since 2i is a root, so is -2i Turn the roots into factors, multiply them together, then use long division Turn the roots into factors, multiply them together, then use long division Then factor to find the remaining roots Then factor to find the remaining roots So the roots are: 3-i, 3+I, 1, and -4 So the roots are: 2i, -2i, 3, and -4

  17. Find the vertical asymptotes, if any, of the graph of each function. x = -2, x = 2 x = 4 No vertical asymptote x = -7

  18. Find the horizontal asymptote, if any, of the graph of y = 1 y = 0 If a monomial is on bottom then you just break it up. Otherwise must do long division y = 1 y = 3x + 3

  19. Choose the correct graph for the rational function

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