This week in Pre-Calc 11, we continued with our analyzing quadratic equations unit. We learnt how to take each equation and write it in standard form, because the way they gave us the equation isn’t helpful to graph it but putting it into standard form makes it possible to graph it.
Example:
Step 1: The first thing we have to do, is make the x by itself, for it to be possible to complete the square. How we are going to do that is take the greatest common factor out of the first two numbers, a way to remember which numbers you take it out of, is if it has a x. In this case I am going to pull out a 2 and that leaves me with x^2 and 4x inside my bracket and we can see the -4 wasn’t effected and stays outside of the bracket.
Step 2: The second step is to find our zero pair we need to add into our equation. How you do that is take the number in front of x, divide it by 2 and then square whatever number you get. That can seem like a lot of work but in this case, you have 4. Divide that by 2 and you get 2, 2 squared is 4. And then you have to add in a zero pair, meaning you need to add +4, -4 into the brackets.
Step 3: Now I need to get my -4 out of the bracket. But to do that I need to multiply it with the 2 out front of my bracket. And the combine my -4 with the -8 I will get when 2 multiplies with the -4 from inside of the bracket.
Step 4: Our final step is to fix our bracket. You’re going to go back to the number you got when you divided it by 2 and put that into your bracket. In this case when I divided 4 by 2 I got 2, so that is the number I am putting back into my bracket and everything in this bracket is positive therefor it’s going to be +2, but if the number was negative you would put -2. It depends what is in the brackets you’re starting with.
Once you get your equation into this form it is ready to graph. In my opinion the most important step is when you’re adding in your zero pair and that is where I would go back and double check you did it correct because if not it will mess up your whole equation. But that is it! All you need to do now is identify the clues I talked about in my last blog post and graph this.
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