MATH 100 Quiz 5

You may use a calculator on this quiz. You may not use a cell phone or computer. If you wish partial credit for incorrect answers, please show your work carefully and give justifications for your answers. If you find that you are spending a lot of time on one problem, leave it blank and move on to the next. There are questions on both sides of this page.
  1. (10 points; 2.1:5) Simplify: (-3+i)(-3-i)
    (Remember that i2 = -1.)







  2. (20 points; 2.3:8) For the polynomial function whose graph is shown on the right:

    a) Is the leading coefficient positive or negative?



    b) Is the degree odd or even?



    c) True or false: (x-2) is a factor.



    d) Does the zero at x=1 have odd or even multiplicity?




  3. (35 points; 2.2:6) The graph of the function f(x) = -3x2 + 12x - 6 is a parabola. Give the coordinates of the vertex of this parabola. (Your answer should be of the form (x,y).)





  4. (2.6:2) Show your work as you answer questions about the following rational function:
    H(x)= -3x2

    a) (10 pts) What is the domain of H(x)?



    b) (10 pts) For what values of x does H(x) = 0?



    c) (5 pts) What are the vertical asymptotes of the graph of H(x), if any?



    d) (10 pts) What are the horizontal asymptotes of the graph of H(x), if any?



Bonus (5 points) If the sum of two numbers is 72, what is the largest value the product of those two numbers can have? Expain your reasoning.