Hey there everybody it's Angelique,

Today during class we learned about factoring to find zeros. While we were going over this in the workbook it showed that when a quadratic is not factorable, sometimes it is possible to find the zeros by completing the square then solving for x. This method is best used when a quadratic does not factor, the middle term is even, and if the value of k is negative, then you will have to complete the square first to know this information.

For Example :
To find the zeros of y = (x+3)² -14

First you change the y into a 0 so then the equation would be 0 = (x+3)² -14

Then the next step is to bring the -14 over to the other side of the equal sign making it positive and now the equation would look like this 14 = (x+3)²
Now you would square root both sides to look like this ±√14 = √(x+3)²
because there is a square root sign over the (x+3)² the squared out side the bracket would cancel with the square root and then now the equation would be ±√14 = x+3

Then you would bring the +3 to the other side of the equal sign and become negative. The equation should now look like this -3 ±√14 = x

Now these are your zeros x = -3 ±√14 or also x = -3 -√14 and x = -3 +√14

Also today we were assigned our groups for the Principia Mathematica Project and got to choose what topic our groups wanted to do and got our first assignment on quadratic functions. Well that's all for now !

HOMEWORK -
Complete the Square Worksheet 2
Exercise 5, Questions 1, 2, 6, and 8