Monday, September 29, 2008

Today in class we went over Homework 12. Then we took notes on solving equations, either algebraically or graphically on the worksheet page 380 on the Section Exercises 5.4:

• For question 1d. in Homework 12, one possible solution Mr. Marchetti showed us was the function
  

3. By graphing each side of this problem on the calculator with the first half of the problem before the equal sign as y1 and the 8 as y2 we were able to tell that these two equations intersected at x=.1621 and x=1.46, which is the solution



Unfortunately, the graphing method only gives approximations so it is better used as a way to check your answers.



6. We also solved this problem graphically in class to find intersections at x=2 and x=-7
If this problem were an inequality like this , the solution would be x<-7 Then we learned how to solve a problem algebraically: 2. To solve this problem, both sides have to be multiplied by (x-4) to eliminate the fraction




So then the equation looks like:




To finish solving, bring the 5x to one side and the 3 to the other:



-4x=-23 Then divide both sides by -4 so







10. The first step would be to factor wherever possible, so the new equation would be:


The next step would be to multiply each side by (x+4)(x-1)





After distribution, all like terms are gathered.





Since this equation is quadratic, 15 can be subtracted from both sides to make one side zero and the other side can be factored and solved from there.





To make one of the sides zero so the equation will be equal to zero,


or





The first answer to this problem is not relevant unfortunately, because the x=1 in the second fraction would be:

Which doesn't make sense because it is not possible to divide by zero. This problem can be checked by graphing the system which shows that at x=1, there is a vertical asymptote so it is not a possible anyswer, which is called an extraneous solution.



Homework:

• Worksheet page 380 choose 2 problems from Section Exercises 5.4 from questions 1-8 and choose 3 problems from questions 9-19. Solve each algebraically and then check them graphically.


• PoW 8 due any day from Thursday to Tuesday


• There is a quiz over functions on Thursday 10/9

The next scribe will be Maddy.