Hey guys, it's Richard.

Today in class we started off by looking at another mathematical picture that Mr.P had for us on the projector. It was a picture of mountains which, if you looked closely, had a parabola in it. It was pretty cool. Mr.P always has new, cool pictures everyday. We then looked at page 25, example 4 in the booklet which Mr.P mentioned is going to be on the test. I'm glad he went over it because I actually didn't know how to do it.

Example 4 (Page 25)
You had to find the equation of the quadratic function given its vertex which was at (1,1) and a point on the graph which was at (4,7), which actually means to find A.

First, you had to use the equation y= a(x-h)² + k then substitute x ,h ,y and k which are actually your vertex (1,1) = (h,k) and your point that was given (4,7) = (x,y).

So when you substitute, it'll look like this 7 = a(4-1)² + 1. Then do what's in the brackets (4-1=3) and then bring the 1 over to the other side and switch the sign so it would then look like 7-1 = a(3)². Then subtract the left side, and square the right side so you'll get 6=a9. Bring the 9 over to the other side and it'll be   = a which then reduces to a=  which then could be substituted for (a) which would make the equation look like:
y= (x-1)² + 1.



We also went through page 29 & 30 in the booklet and one of the difficult questions was c) because it had a negative in it. Here's how we did it:

c) (Page 31)
y= -x + 6x + 2

Equate it to 0 so it looks like this: 0 = -x² + 6x + 2
Bring the 2 over to the other side and switch the sign: -2 = -x² + 6x
Factor in the negative: -2 = -(x-6x)
Complete the square so take -6, divide it by 2 and square it so you get 9, then add it to the equation but for the left side you must take the 9 and multiply it by the negative since it's in the place for A so for the left side it would be -9 and it would look like this: (-2) -9 = -(x² -6x +9 )
Bring the -2 and the -9 to the other side and it becomes 0 on the left again: 0 = -(x² -6x +9) +2 +9
Factor and simplify and bring back the y: y = - (x-3)² + 11 and that's your final answer!

Make sure you remember that one because it may be on the test as well!

Homework


We had a lot of homework, but it's helping us for the test coming up on Friday, Oct. 1st! There was "Complete the Square Worksheet #3", a "Practice Mix bag" paper with pretty much questions on everything we've covered in the quadratic function unit, you don't have to do it all by the way! Just the difficult ones that Mr.P was calling out in class today. We also have a review, but isn't due till next week, but it may be a good idea to go over it so we're fresh in memory for it on the test on Friday!