Project #87827 - pre-calculus

 Quadratic fluntion answer all the questions in Menu A .  f(x) = 3x2 + 3x - 1

Polynomial funciton answer all the questions Menu B.  f(x) = -x5 - x3 + 6x

 

Questions for Menu A Functions                      Questions for Menu B Functions
 1. Without graphing the function, determine whether the parabola opens upward or downward.  How do you know?  1. Without graphing the function, determine the end behavior of the graph.  Refer to my End Behavior Chart and use the correct letter (A, B, C, or D) to state your answer.  How did you determine your answer?
 2. Find the vertex of the parabola, using the vertex formula open parentheses fraction numerator minus b over denominator 2 a end fraction comma space f open parentheses fraction numerator minus b over denominator 2 a end fraction close parentheses close parentheses . Show your work.  2. If the polynomial is not already in factored form, factor it completely.  What are the x-intercepts of the polynomial? (Note: #13 and #14 require you to use the concepts of sections 2.4 and 2.5 to factor; you may use other factoring techniques on #1 - 6 and #12)
 3. Without graphing the function, determine whether it has a maximum or a minimum value?  How do you know?  State the maximum function value or the minimum function value.  State the value of x where this maximum or minimum occurs.  3. Multiplicity of zeros is explained in your book on page 324.  Does your polynomial function have any zeros of multiplicity 2 or more?  If so, state each zero and its multiplicity.  Explain how the graph of a polynomial behaves when it has a zero of even multiplicity.  What happens if it has a zero of odd multiplicity?
 4. Write the function in the standard form f(x) = a(x - h)2 + kwithout completing the square! How did you know what to use for a, h, and k?  4. What is the maximum number of turning points that your graph may have?  Base your answer on the degree of the polynomial - do not look at the graph!
 5. Without graphing the function or attempting to find the x-intercepts, determine whether the parabola has x-intercepts or not. How can you tell?  5. Find the y-intercept of the graph.
 6. If the parabola has x-intercept(s), solve f(x) = 0 to find them. Show your work.  6.  Sketch a picture of the graph of your polynomial function on your own paper.  Then graph the function on your calculator or using the website http://graphsketch.com/. Does your sketch look like the graph on your calculator? If not, describe how your sketch is different. Capture a picture of the graph from your calculator or by downloading the graph from thegraphsketch.com website. Attach the graph to your primary input message on the discussion board.
 7. Find the y-intercept.  7.  You can use the CALC menu on your TI-83 or TI-84 calculator to locate the relative (local) maxima and relative (local) minima on your graph.  Review page 175 of your book to remember what the terms "relative maximum" and "relative minimum" mean.  Watch this video on YouTube to learn how to find the relative (local) maxima and relative (local) minima of your graph using your calculator: www.youtube.com/watch?v=xTofCWXtYyU. Although the narrator says you can go "anywhere" to the left and right of the desired point to set left and right bounds, you should actually set your left and right bounds as close to the desired point as possible. What are the relative maxima and relative minima of the graph of your function?  You may state each answer as an ordered pair.  Be sure to specify whether each ordered pair is a maximum or a minimum.  
 8. State the range of the function in interval notation.  State the axis of symmetry in the form "x = ___".  Describe how to answer these questions without graphing the function.
 9. Graph the function and capture a picture of the graph to attach to the discussion board.  You may use graphing calculator emulator software, take a digital picture of your graphing calculator screen, or go to the websitehttp://graphsketch.com/ to graph the parabola and download your graph.
10. Complete the following statement:  "To move from the vertex on the graph of my parabola to the point on the graph whose x-coordinate is 1 more than the x-coordinate of the vertex, I would need to move one unit to the right and  _______ units ______________."  In the first blank you will insert a number (may be a fraction).  In the second blank, you will either write "upward" or "downward", whichever word is appropriate. 8. Using your graph and your answers to the previous question, state the range of your polynomial function in interval notation.
9. State the intervals on which the function is increasing and the intervals on which it is decreasing. Review section 1.3 to brush up on the concepts of increasing and decreasing functions, if necessary. 

Subject Mathematics
Due By (Pacific Time) 10/19/2015 09:00 pm
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