Chapter 5 Closure – Portfolio

How many different kinds of graphs can you create that have:

1. No x-intercepts?
   1. Quadratic
      1. 
      2. The Equation is y = 0.49(x + 1.1)^2 +5.62
      3. The Locator Point is at (-1.1, 5.62) and it will never touch the x-axis
   2. absolute value
      1. 
      2. The equation is y = 2|x – 5.5|+ 4.23
      3. The locator point is (5.5, 4.23) and it never touches the x-axis
   3. Rational
      1.  
      2. The equation of this is y = 0.5/x-2
      3. There is no locator point for this graph
      4. There are two asymptotes for this graph. one at x = 2 and y = 0
         1. Since there is an asymptote at y = 0 the lines never cross the x-axis
   4. Exponential
      1.   
      2.  The equation is f(x) = 2(2)^(x – 6) +5.65
      3. The locator point for this graph is at (0, 5.681)
         1. The line will never cross the x-axis so there is no x-intercept
      4. there is an asymptote at y = 5.65
   5. square root
      1.  
      2. The equation is y = 2sqrt{x+2}+1
      3. The locator point is at (-2, 1)
         1. it will never cross the x-axis
2. One x-intercept?
   1. Quadratic
      1.  
      2. The Equation is y = 0.49(x + 1.1)^2
      3. The locator point is (-1.1, 0)
         1. This is also the only x-intercept
   2. Absolute value
      1.  
      2. the equation is y = 2|x – 5.5|
      3. The locator point is (5.5, 0)
         1. This is also the sole x-intercept
   3. Exponential
      1.  
      2. The Equation is 2(2)^(x-6) – 1
      3. The locator point is at (0, -1)
      4. The sole x-intercept is at (5, 0)
   4. Rational
      1.  
      2. y = .05/(x-2) + 2
      3. There is no locator point
      4. There are two asymptotes
         1. one at y = 1.975 and x = 1.975
      5. The singular x-intercept is at (1.975, 0)
   5. Cubic
      1.  
      2. y = 2(x + 1)^3 + 4.6
      3. the locator point is (0, 6.6)
      4. The single x-intercept is (-2.32, 0)
   6. Cubed Root
   7. linear
      1.  
      2. The equation is y = 3x +2
      3. The locator point is at (0, 2)
      4. the sole x-intercept is at (2/3, 0)
   8. Square root
      1.  
      2. the equation is y = 1.35sqrt(x + 1.8)
      3. The locator point is (-1.8, 0)
         1. This also the x-intercept
3. Two x-intercepts?
   1. Quadratic
      1.  
      2. The equation is -0.49(x + 1.1)^2 + 5.62
      3. The locator point is at (-1.1, 5.62)
      4. The line has two x-intercepts at (-4.487, 0) and (2.287, 0)
   2. Absolute Value
      1.  
      2. the equation is y = 2|x – 5.5|-1
      3. The locator point is at (5.5, -1)
      4. The two x-intercepts are (5, 0) and (6, 0)
   3. Cubic
      1.  
      2. The equation is y = x^3 -2x + 1.1
      3. The locator point is (0, 1.1)
      4. the two x-intercepts are (-1.635, 0) and (0.816, 0)
4. Three or more x-intercepts?
   1. Cubic
      2. 
      3. The equation is y = x^3 -2x -1
      4. The locator point is at (0, -1)
      5. The three x-intercepts are (-1, 0), (-0.618, 0), and (1.618, 0)

Closure 3 #3

This section gives you an opportunity to show growth in your understanding of key mathematical ideas over time as you complete this course.

Your team has been assigned the task of preparing a set of directions for future algebra students on how to perform operations with rational expressions.  Your assignment is to select one rational expressions addition or subtraction problem and one rational expressions multiplication or division problem from the chapter.  Show step-by-step how to do the two problems you have selected.  Next to each step, include an explanation of why you are making that step.  You want to be sure your result is correct, so use a graphing tool to check your answer by comparing the graph of the original problem and with the graph of your answer.

A student who has just enrolled in an Algebra 2 class needs help understanding why (x + y)² = x² + 2xy + y².  She thinks that (x + y)² = x² + y².  Justify why (x + y)² = x² + 2xy + y²  so that she is convinced that your answer is correct.

(x + y)² doesn’t equal x² + y² because there is addition inside the parenthesis. if there was multiplication inside the parenthesis is would then be xy times xy, but since there is addition it is actually (x+y) times (x+y) so you have to factor it out. When it is factored out it equals x² + 2xy + y².