Test # 3 Review. È 3. Compare the graph of n 1 ÎÍ. Name: Class: Date: Short Answer. 1. Find the standard form of the quadratic function shown below:

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1 Name: Class: Date: ID: A Test # 3 Review Short Answer 1. Find the standard form of the quadratic function shown below: 2. Compare the graph of m ( x) 9( x 7) 2 5 with m ( x) x 2. È 3. Compare the graph of n 1 ÎÍ 3 ( x 4) 2 8 with n( x) x From the graph of the quadratic function f ( x) ( x 2) 2 9, determine the equation of the axis of symmetry. 5. Determine the x-intercept(s) of the quadratic function f ( x) x 2 10x Determine the x-intercept(s) of the quadratic function f ( x) x 2 4x Determine the vertex of the graph of the quadratic function f ( x) x 2 x From the graph of the quadratic function f ( x) x 2 8x 5, determine the equation of the axis of symmetry. 9. Write the quadratic function f ( x) x 2 4x 3 in standard form. 10. Write the quadratic function f ( x) x 2 2x 2 in standard form. 1

2 Name: ID: A 11. Write the quadratic function f ( x) 1 8 x 2 16x 8 in standard form. 12. Write the standard form of the equation of the parabola that has a vertex at ( 8, 3) and passes through the point ( 6, 2). 13. Write the standard form of the equation of the parabola that has a vertex at through the point ( 1, 2). 2 3, 1 9 and passes 14. Find two positive real numbers whose product is a maximum and whose sum is A farmer has 336 feet of fencing and wants to build two identical pens for his prize-winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area. 16. Find all real zeros of the polynomial f ( x) x 3 6x 2 9x 54 and determine the multiplicity of each. 17. Find all real zeros of the polynomial f ( x) x 4 5x 3 6x 2 and determine the multiplicity of each. 18. Find all real zeros of the polynomial f ( x) x 4 52x and determine the multiplicity of each. 19. Using a graphing utility, graph f ( x) x 3 4x and approximate the zeros and their multiplicity. 20. Use long division to divide. x 3 5x 2 16x 80 ( x 5) 21. Use long division to divide. x 3 8 ( x 2) 2

3 Name: ID: A 22. Use synthetic division to divide. 4x 3 x 2 11x 6 ( x 2) 23. Use synthetic division to divide. 24 5x 3 22x 27x 2 ( x 2) 24. Use synthetic division to divide. x 3 27x 54 ( x 3) 25. Write f ( x) x 3 3x 2 3x 32 in the form f ( x) ( x k )qx ( ) r when k If f ( x) 3x 2 4x 1, use synthetic division to evaluate f () If x 1 is a root of x 3 4x 2 x 4 0, use synthetic division to factor the polynomial completely and list all real solutions of the equation. 28. If x 7 is a root of x 3 3x 2 7x 21 0, use synthetic division to factor the polynomial completely and list all real solutions of the equation. 29. Using the factors ( x 5) and ( x 2), find the remaining factor(s) of f ( x) x 3 6x 2 3x 10 and write the polynomial in fully factored form. 30. Using the factors ( 3x 2) and ( x 1), find the remaining factor(s) of f( x) 6x 4 23x 3 12x 2 11x 6 and write the polynomial in fully factored form. 31. Simplify the rational expression, 3x 3 x 2 40x 48, by using long division or synthetic division. 3x Find all zeros of the function f ( x) x 2 ( x 2) x Find all zeros of the function f ( x) ( x 2) ( x 3i) ( x 3i). È 34. Find all zeros of the function f ( x) ( x 4) ( x 3) ÎÍ x ( 4 3i). È ÎÍ x ( 4 3i) 35. Find all the rational zeros of the function f ( x) 2x 5 3x 4 9x 3 3x 2 11x 6.. 3

4 Name: ID: A 36. Given 5i is a root, determine all other roots of f ( x) x 3 5x 2 25x Given 1 i is a root, determine all other roots of f ( x) x 5 8x 4 24x 3 32x 2 20x. 38. Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f ( x) x 5 2x. 39. Use Descartes' Rule of Signs to determine the possible number of positive and negative zeros of f ( x) x 3 4x 2 6x Find all the real zeros of f ( x) 6x 3 8x 2 6x 8. 4

5 ID: A Test # 3 Review Answer Section SHORT ANSWER 1. ANS: f ( x) 3( x 1) 2 PTS: 1 REF: 78 OBJ: Determine the standard form of a quadratic function 2. ANS: m ( x) 9( x 7) 5 shifts right 7 units, shifts upward 5 units, and stretches by a factor of 9. PTS: 1 REF: 67 OBJ: Compare transformed graph to base graph 3. ANS: n( x) È 1 2 ÎÍ 3 x 4) 8 shifts left 4 units, shifts downward 8 units, and shrinks by a factor of 1 9. PTS: 1 REF: 68 OBJ: Compare transformed graph to base graph 4. ANS: x 2 PTS: 1 REF: 71 OBJ: Determine axis of symmetry 5. ANS: no x-intercept(s) PTS: 1 REF: 73 OBJ: Determine x-intercepts of quadratic function 6. ANS: ( 4, 0), ( 8, 0) PTS: 1 REF: 74 OBJ: Determine x-intercepts of quadratic function 7. ANS: 1 2,1 PTS: 1 REF: 70 OBJ: Determine vertex of quadratic function 8. ANS: x 4 PTS: 1 REF: 72 OBJ: Determine axis of symmetry 9. ANS: f ( x) ( x 2) 1 PTS: 1 REF: 76 OBJ: Write quadratic function in standard form 1

6 ID: A 10. ANS: f ( x) ( x 1) 2 3 PTS: 1 REF: 75 OBJ: Write quadratic function in standard form 11. ANS: f ( x) 1 8 ( x 8)2 7 PTS: 1 REF: 77 OBJ: Write quadratic function in standard form 12. ANS: f ( x) 5 4 ( x 8)2 3 PTS: 1 REF: 79 OBJ: Write standard form of a parabola 13. ANS: f ( x) x PTS: 1 REF: 80 OBJ: Write standard form of a parabola 14. ANS: 78, 78 PTS: 1 REF: 81 OBJ: Application: Quadratic functions 15. ANS: 42' 56' PTS: 1 REF: 83 OBJ: Application: Quadratic functions 16. ANS: x 3, multiplicity 1; x 3, multiplicity1; x 6, multiplicity 1 PTS: 1 REF: 90 OBJ: Determine zeros and multiplicity 17. ANS: x 0, multiplicity 2; x 3, multiplicity 1; x 2, multiplicity 1 PTS: 1 REF: 92 OBJ: Determine zeros and multiplicity 18. ANS: x 4,multiplicity 1; x 4, multiplicity 1; x 6,multiplicity 1; x 6,multiplicity 1 PTS: 1 REF: 91 OBJ: Determine zeros and multiplicity 19. ANS: x 0, multiplicity 1; x 2, multiplicity 1; x 2, multiplicity 1 PTS: 1 REF: 93 OBJ: Approximate roots with graphing utility 20. ANS: x 2 16 PTS: 1 REF: 98 OBJ: Divide polynomials using long division 2

7 ID: A 21. ANS: x 2 2x 4 PTS: 1 REF: 99 OBJ: Divide polynomials using long division 22. ANS: 4x 2 7x 3 PTS: 1 REF: 102 OBJ: Divide polynomials using synthetic division of polynomial 23. ANS: 5x 2 17x 12 PTS: 1 REF: 103 OBJ: Divide polynomials using synthetic division of polynomial 24. ANS: x 2 3x 18 PTS: 1 REF: 104 OBJ: Divide polynomials using synthetic division of polynomial 25. ANS: f ( x) ( x 5) x 2 2x 7 3 PTS: 1 REF: 107 OBJ: Rewrite polynomial: quotient and remainder 26. ANS: f () 4 63 PTS: 1 REF: 109 OBJ: Evaluate using synthetic division 27. ANS: ( x 4) ( x 1) ( x 1); x 4, 1, 1 PTS: 1 REF: 111 OBJ: Factor using synthetic division 28. ANS: ( x 3) x 7 x 7 ;3, 7, 7 PTS: 1 REF: 113 OBJ: Factor using synthetic division 29. ANS: f ( x) ( x 5) ( x 2) ( x 1) PTS: 1 REF: 114 OBJ: Factor polynomial given factor(s) 30. ANS: f ( x) ( 3x 2) ( x 3) ( 2x 1) ( x 1) PTS: 1 REF: 115 OBJ: Factor polynomial given factor(s) 3

8 ID: A 31. ANS: x 2 x 12 PTS: 1 REF: 117 OBJ: Approximate roots with graphing utility 32. ANS: x 0, 2, 6, 3 3 3i, 3 3 3i PTS: 1 REF: 119 OBJ: Determine zeros of polynomial 33. ANS: x 2, 3i, 3i PTS: 1 REF: 120 OBJ: Determine zeros of polynomial 34. ANS: x 4, 3, 4 3i, 4 3i PTS: 1 REF: 121 OBJ: Determine zeros of polynomial 35. ANS: x 1 2, 3,2 PTS: 1 REF: 123 OBJ: Determine zeros of polynomial 36. ANS: x 5, 5i PTS: 1 REF: 129 OBJ: Approximate zeros with graphing utility 37. ANS: x 3 i, 1 i,0 PTS: 1 REF: 131 OBJ: Determine zeros of polynomial 38. ANS: no positive reals; no negative reals PTS: 1 REF: 135 OBJ: Apply Descartes' Rule of Signs 39. ANS: 3 positive reals or 1 positive real; no negative reals PTS: 1 REF: 136 OBJ: Apply Descartes' Rule of Signs 40. ANS: x 4 3 PTS: 1 REF: 139 OBJ: Determine zeros of a function 4

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