I know y = (x^2 - 12x + 36) - 36 +7 factored becomes y = ( (x - 6)(x - 6) ) - 36 + 7, but what is the step by step method for doing this? Please be clear and concise (no short cuts!), I need a better understanding of this process.
I know y = (x^2 - 12x + 36) - 36 +7 factored becomes y = ( (x - 6)(x - 6) ) - 36 + 7, but what is the step by step method for doing this? Please be clear and concise (no short cuts!), I need a better understanding of this process.
I am only going to use distributive law... twice.So watch carefully,
x^2 - 12x + 36
= x^2 - 6x - 6x + 36
= x(x - 6) - 6(x - 6) <-------- First time I used distributive law(Err.. I used it twice in one go)
= (x - 6)(x - 6)<--------- Second time... I factored the common (x - 6) out
If you find it hard, try replacing (x - 6) by y and then you will see it easily
This is going to sound like a very dumb question, but why is only (x^2 - 12x + 36) factored in the equation y = x^2 - 12x + 36 - 36 +7 ? Why not factor every part of it?
I don't mean to annoy with that question, it just seems like everyone besides me knows why everything is done in math and I'm always sitting there wondering. It's like I'm always missing a piece of the puzzle, but when I find it I understand immediately. Does that make sense?
Its not a dumb question at all. We cant point out the reason unless you post the complete problem and the part where this happened.
However if I were to guess, you were most likely solving the quadratic x^2 - 12x + 7 = 0 OR factorising x^2 - 12x + 7 using "complete the square" trick.
So give the context of the step and we will tell you why they did it that way...
Thats possibly practice and lack of initiative. If you stay at a problem for a long time, work out similar looking questions(I mean worked out examples), most text book problems will be easy. So just keep practicing with a keen eye and a sharp mind.I don't mean to annoy with that question, it just seems like everyone besides me knows why everything is done in math and I'm always sitting there wondering. It's like I'm always missing a piece of the puzzle, but when I find it I understand immediately. Does that make sense?
It was a "completing the square" question.
And thanks for responding to the other part of my post. That's good advice. I always feel like I'm cheating when I look at the text book examples though.
I've had trouble with math in the past so I put a lot of pressure on myself when doing it now. I guess I just need to take it easy!
I would guess that also, Iso.
Problem: Convert the parabola $\displaystyle y=x^2-12x+7$ into vertex form.
Complete the square:
$\displaystyle y=(x^2-12x +\_\_\_)-\_\_\_+7$
Take half the coefficient of x, square it, and add it to make a perfect square trinomial. But you have to subtract it also to keep the equation balanced.
$\displaystyle y=x^2-12x+6^2-6^2+7$
$\displaystyle y=(x-6)^2-29$
The parabola opens up and has a vertex (6, -29).
More information, but I didn't want to be too redundant.