What was the hardest math subject of the year for me? Well, I understood almost everything we learned in Algebra, but there is probably one thing that took me a while to understand. And that was the quadratic formula. I know it by heart know: -b+/-

When you have an equation like x^2+4x+4, you can easily factor this to (x+2)^2=0. This gives you x=-2 . But, if you have an equation like x^2+4x+3, you would have to complete the square, meaning you would have to add 1 to both sides of the equation. So now the equation is x^2+4x+4=1. Now you factor, and you get (x+2)^2=1. Now square root both sides so that you get x+2=+/- 1 ( The square root of one gives you 1 ). So you solve both equations, and you get x=-3 and x=-2. Pretty easy, right? Now for the fun part. And when I say fun, I mean hard. So what happens when you get a problem with no complete square? Let's do the problem x^2+11x+5=0. Well, you can't factor it just like that, and you can't create a perfect square for it. So let's see what we get by plugging in the quadratic formula. a=1, b=11, and c=5. -11+/-

*the square root of*b^2 -4ac/2a. It's difficult to type the quadratic formula, but just bear with me. I'm sure why you can see I was pretty confused with this equation. We were working with the equation of parabolas, ax^2+bx+c. I understood this equation, but when Mr. Erickson introduced the quadratic formula, I didn't really understand why we had to use it. It was a long while until Mr. Erickson showed us exactly why we needed this equation. This is why:When you have an equation like x^2+4x+4, you can easily factor this to (x+2)^2=0. This gives you x=-2 . But, if you have an equation like x^2+4x+3, you would have to complete the square, meaning you would have to add 1 to both sides of the equation. So now the equation is x^2+4x+4=1. Now you factor, and you get (x+2)^2=1. Now square root both sides so that you get x+2=+/- 1 ( The square root of one gives you 1 ). So you solve both equations, and you get x=-3 and x=-2. Pretty easy, right? Now for the fun part. And when I say fun, I mean hard. So what happens when you get a problem with no complete square? Let's do the problem x^2+11x+5=0. Well, you can't factor it just like that, and you can't create a perfect square for it. So let's see what we get by plugging in the quadratic formula. a=1, b=11, and c=5. -11+/-

*the square root of*(-11)^2 -4(1)(5)/2(1).*-11^2 is 121, so 121-20=101, and the square root of 101 is 10.0498... but we'll round it to 10. So now we have -11+/- 10/2=x. -11+10=-1, divided by 2 is -.5. -11-10=-21, and divided by two is -10.5. So now you know that x=-10.5 and x=-.5. It seems very complicated, but after doing problems like this and seeking help from Mr.Erickson and friends, I was finally able to understand the quadratic formula.*