Question

I suck at writing stuff like this out... could anyone help me?
Part 1: Solve each of the quadratic equations below and describe what the solution(s) represent to the graph of each. And I'm supposed to show my work.
y = x2 + 3x + 2
y = x2 + 2x + 1
Part 2:Using complete sentences, answer the following questions about the two quadratic equations above.
Do the two quadratic equations have anything in common? If so, what?
What makes y = x2 + 3x + 2 different from y = x2 + 2x + 1?
Any help would be greatly appreciated :)

Answer 1

Let's look at the first one for an example. To factor them out you have to think "Alright, what two factors of 2 add to make 3?" Well, that's just 2*1=2 and 2+1=3 so you know you have a winner. It'll take some practice until you don't have to think about it too hard so don't get frustrated if you don't get it right away.

Then once you've done that you can say that the first will be (x+1)(x+2) because of what we just did. Now if you don't believe me or understand why, I strongly suggest just FOILing them back out to your original answer to see that it is indeed the same answer!

I believe you can see why FOIL is the reverse of factoring and why you have the two terms added and the one term multiplied to understand why.

Upon factoring you can see what factor they have in common and which one they don't for your answer, as I'm assuming that's what they're expecting for you to say the difference is between them even though it's kind of vague.

Answer 2

Alright, thank you. :)