Information about Test 2

• Reminder: There is a test on Wednesday, September 30. It will take the full 50 minutes and covers Sections 1-4 of Chapter 2, as well as questions from Quiz 1 and Quiz 2. Again, because this test has many graphing questions, NO CALCULATORS will be allowed.

  The important topics covered in sections 1-4 of Chapter 2 are:

  1. Quadratic Functions --- Complete the square to put into standard form

      
          y = a(x-h)^2 + k
     

     and then graph by analyzing in terms of reflection, stretching, vertical and horizontal shifts

  2. Polynomials of Higher degree --- Know what the graphs of

         y = x^2,  y = x^3,   y = x^4,   y = x^5, ..., y = x^n
     

     look like. By analyzing reflection, stretching, vertical and horizontal shifts be able to graph anything of the form

     y = a(x-h)^n + k
     

     Or if you have a factored polynomial such as

         f(x) = (x-2)(x+1)(x+1)(x-5)(2x + 3)
     

     be able to graph it by analyzing the intercepts, where y=f(x) is positive and where y = f(x) is negative. You may also find the leading coefficient test useful.

  3. Polynomial and Synthetic division

  4. Finding Real zeros of Polynomials
     • Use the factors of the leading coefficient and the constant term to make a list of possible rational zeros.

     • Use synthetic division to evaluate the polynomial at these points. In many cases this will lead to a complete factorization of the polynomial. Keep your eyes open for sign changes because this can help you make more efficient choices when you decide which potential root to check next.

     • If you can factor the polynomial, then you can sketch its graph.

  5. The test may also include material from Quiz 1 and Quiz 2. These questions will take the form of small variations on the questions that were on the quizzes. So to prepare for these questions, you should study the solutions to these quizzes, and make sure you know how to work the problems that appeared there.