Project 3 - 8 questions

(0) Develops a strategy to solve the problem Clearly applies the strategy provided to solve the problem. (2) Applies a strategy to solve the problem that is appropriate. (1) Does not apply the strategy to solve the problem. (0) Applies appropriate procedures throughout the solution process Completely applies appropriate and efficient procedures and/or strategies throughout the solution process to determine the characteristics of a polynomial (or quadratic or rational) function. (3) Applies appropriate and efficient procedures and/or strategies for determining most of the characteristics (or all of the characteristic with minor errors) of the polynomial (or quadratic or rational) function. (2) Applies appropriate and efficient procedures and/or strategies for determining some of the characteristics (or most of the characteristic with minor errors) of the polynomial (or quadratic or rational) function. (1) Does not apply appropriate and efficient procedures and/or strategies for determining any of the characteris tics of the polynomial (or quadratic or rational) function. (0) Graphical representation and solution of the problem. Clearly and accurately graphs the polynomial (or quadratic or rational) function. The graph is elegant, complete, and correct. (3) Acc urately graphs the polynomial (or quadratic or rational) function. The graph is complete and correct. (2) The graph of the polynomial (or quadratic or rational) function is partially complete or partially correct. (1) The graph of the polynomial (or quadra tic or rational) function is incomplete and incorrect. (0) Project Chapter 3, sections 1 -5, page 2 For q uestions 1 and 2 , do steps 1 -7 below. A quadratic function of the form ()= 2+ + (1) Determine if the parabola opens upward or do wnward. (3) Identify the vertex . (do before part 2) (2) Determine the minimum or maximum value of the parabola . (4) Identify the axis of symmetry . (5) Identify the y -intercept . (6) Identify the x-intercept(s) . (7) Graph the parabola . A quadratic function of the form ()= (− ℎ)2+ (1) Determine if the parabola opens upward or downwar d. (2) Determine the minimum or maximum value of the parabola . (3) Identify the vertex . (4) Identify the axis of symmetry . (5) Identify the y -intercept . (6) Identify the x-intercept(s) . (7) Graph the parabola . 1. Do steps 1 -7 above given the quadratic function. Show all your work and organize your findings in the table provided. ()= 2− 2− 3 (1) Opens upward or Downward_______________________ (3) Vertex______________________ (2) Minimum or maximum_______________________ (4) Axis of symmetry______________________ (5) y -intercept______________________ (6) x -intercept(s)______________________ Project Chapter 3, sections 1 -5, page 3 2. Do steps 1 -7 above given the quadratic function. Show all your work and organize your findings in the table provided. ()= (+ 2)2− 1 3. Solve the inequality using the test -point method. State the solution set in interval notation. 2− 2− 24 > 0 (1) Opens upward or Downward_______________________ (2) Minimum or maximum_______________________ (3) Vertex______________________ (4) Axis of symmetry______________________ (5) y -intercept______ ________________ (6) x -intercept(s)______________________ Project Chapter 3, sections 1 -5, page 4 4. Do the following steps for the given polynomial function: (1) Use the Rational Zero Theorem to find all possible rational zeros, (2) Check possible zeros found in step 1 using synthetic division until you find a zero, and (3) Find all the zeros (hint: by factoring the quotient from step 2) ()= 3− 32− 6+ 8 5. Find the polynomial equation with real coefficients that has the root 4+ 2. Hint: there is another root that is not listed, the complex conjugate of 4+2. (1) Possible zeros_____________________ (3) List all the zeros of the polynomial function ___________________________________ Project Chapter 3, sections 1 -5, page 5 6. Do steps 1 -6 below, given the polynomial function. Show all your work and organize your findings in the table provided. ()= 3+ 42 Strategy for Graphing a Polynomial Function (page 306): (1) Check for symmetry (by finding (−)) (2) Find all real zeros of the polynomial function (3) Determine the behavior at the corresponding x -intercepts . (4) Determine the behavior as → ∞ and → −∞ (5) Calculate the y -intercept . (6) Draw a smooth curve through the points to make the graph . (1) Symmetry:__________________________ (2) zeros_______________ x -intercepts ______________ (3) For each x -intercept fill in the blanks of the following at_______the graph ____________ the x -axis at_______the graph ____________ the x -axis (4) as → ∞, ()→ ________ and as → −∞, ()→ _______ or as the graph goes to the right, it also goes ________ and as the graph goes to the left, it also goes_________. (5) y -intercept___________ ___ Proj ect Chapter 3, sections 1 -5, page 6 7. Do steps 1 -5 below, given the polynomial function. Show all your work and organize your findings in the table provided. ()= 2− 3 − 2 Graphing Rational Expressions (pg. 319): (1) Determin e the asymptotes and draw them as dashed lines . (2) Check for symmetry (we will omit this step) (3) Find any intercepts (4) Plot several selected points to determine how the graph approaches th e asymptotes . (5) Draw curves through the selected points, approaching the asymptotes . (1) Asymptotes: __________________________ (3) Intercepts: x -intercepts________________________ y-int ercept________________ (4) T-table determining several points −1 1 4 Project Chapter 3, sections 1 -5, page 7 8. Do the following steps for the given rational function: (1) State the domain (2) reduce the fun ction to lowest terms, (3) determine several points of the function using the given T -table, and (4) Graph the rational function. ()= 2− 8+ 15 − 3 Domain ___________________