Ok, so I was given the points: (5, 1121), (6, 805), (7, 626), (8, 813) (9, 967) Then I'm told to make a scatter plot (which I did) It then says to consider the quadratic model, y=ax^2+bx+c Which means, find a, b, and c in the equation using the points as coordinates. The answer is as follows: "1121=25a+5b+c 626=49a+7b+c 967=81a+9b+c We solve this system of three equations in three variables using procedures of algebra and get: a=104.5 b=-1501.5 and c=6016 Substituting these values into equation (1), we get the function given by y=104.5x^2-1501.5x+6016" My only question is, how the hell did they come up with those numbers? I'm super confused right now.

They solve for c (rearrange it so that c=1121-25a-5b) in equation 1 and substitute it into c for the second equation. The second equation is now in terms of a and b. Then, they solve for b in the second equation and substitute it into b for the third equation. The third equation is now in terms of just a. So with equation 3 they find the value of a, substitute it into equation 2 to find b, and substitute a and b into equation one to get c. To get the original equations, they just use the first, third, and fifth pairs of coordinates. They substitute the (x,y) values into the equation y=ax^2+bx+c.

Haha THANK YOU!!! My brain was just about to explode....and you effectively prevented that from happening. So in a strange way you kind of saved my life Thanks!

I have a very modest questions to you math wizes: What job do you guys have/what do you need to know this type of math for?

Physics, engineering, programming, all of them i have used these exact problems in classes from high school to college, so any career involving that. But everything in the professional world is now computerized, so if you can use CAD you can solve anything.

Pretty much anything scientific field you go into. Or engineering. I'm a few months away from getting my MD in neurobiology and I had to take a computational neuroscience class, that was heavy on higher mathematics. Granted, the question OP posed isn't higher mathematics, but it is still what you would be doing most of in any sort of science class.

Ok wait! I guess I lied...I thought I understood how to do it, but alas after several unsuccessful attempts I still don't get it. Well I get that you are supposed to solve for c and put it in the next equation and so on. But what I am not clear on is how to solve for c? I mean you have c=1121-25a-5b How can you find c if you don't know what a and b are? :S

The solution I gave you before wasn't exactly right, it was a pretty good start though. lol @ the people agreeing with me. 1121=25a+5b+c 626=49a+7b+c 967=81a+9b+c isolate c from eq. 1 c=1121-25a-5b sub c into eq. 2 and isolate b 626=49a+7b+(1121-25a-5b) -495=24a+2b 2b=-24a-495 b=-12a-247.5 substitute c=1121-25a-5b and b=-12a-247.5 into equation 3 967=81a+9(-12a-247.5)+(1121-25a-5b) 967=81a-108a-2227.5+1121-25a-5b 2073.5=-52a-5b isolate b 5b=-52a-2073.5 b=-10.4a-414.7 set b=-10.4a-414.7 and b=-12a-247.5 equal to each other and solve for a -10.4a-414.7=-12a-247.5 1.6a=167.2 a=104.5 plug a into b=-10.4a-414.7 to get b=-1501.5 plug a and b into c=1121-25a-5b to get c=6016 Now please let me get back to my own math homework.