8. Complete the square for the following quadratic functions. (a) x² + 6x-2 (b) 2x² - 8x + 7 (c) 3x² + 6x-5 (d) -1² +41-1

4. What is the constant value (the term without a variable) of the product (3x -1)(2a2 – 6x – 9)?

b. Complete the "Product of a sum and difference" rule. Write a conclusion that describes the relation with "difference of two squares" rule. (a + b)(a- b)- Conclusion: x + 25 c. Verify whether any of these patterns work for the example

The table gives methane gas emissions in millions of metric tons. The quadratic model y = 0.0429x² - 9.73x + 706 approximates the emissions for these years. In the model, x represents the number of years since 2008, so x = 0 represents 2008, x = 1 represents 2009, and so on. Complete parts a and b. Year 2008 2009 2010 2011 2012 Millions of Metric Tons of Methane 706.0 696.3 686.7 677.2 667.8 a. According to the model, what would emissions be in 2014? According to the model, in 2014 the emissions would be 649.2 million metric tons. (Round to the nearest tenth as needed.) b. Find the nearest year beyond 2008 for which this model predicts that emissions will reach 500 million metric tons. The nearest year beyond 2008 for which the model predicts that the emissions will reach 500 million metric tons is (Round down to the nearest year.)