To make this slightly more manageable, let's do a little bit of factoring!
y = a(x^2 + (b/a)x) + c
Still a little freaky... but it's looking better!
Now, let's pretend that our equation only is x^2 + (b/a)x. We have to turn this to (x - h)^2. So let's set it equal!
x^2 + (b/a)x = (x - h)^2
Now, (x-h)^2 in its expanded form is x^2 - 2hx + h^2. So:
x^2 + (b/a)x = x^2 - 2hx + h^2
Looking good! So now, let's subtract the x^2...
(b/a)x = -2hx + h^2
Not good! This show us that we need another term for the other side in order for this to be equivalent! Otherwise, we can't get a constant term! So we're going to add something to this later. Now, let's ignore the h^2 term. We'll figure it out later.
(b/a)x = -2hx
Solve for h!
h = - b/(2a)
So you now now your h!
Now.
y = a(x^2 + (b/a)x + h^2) + c - ah^2
Solve! You will get:
a(x - h)^2 + (c - ah^2)
This is in vertex form.
(Side note: When you learn calculus, this whole process will be much easier.)
Ubi caritas est vera, Deus ibi est.
"The mark of your ignorance is the depth of your belief in injustice and tragedy. What the caterpillar calls the end of the world, the Master calls the butterfly." ~ Richard Bach
Hahaha... yeah, it can get a bit confusing, especially with all the letters in there!
Do you have a specific example I can use? Maybe that will help.
Ubi caritas est vera, Deus ibi est.
"The mark of your ignorance is the depth of your belief in injustice and tragedy. What the caterpillar calls the end of the world, the Master calls the butterfly." ~ Richard Bach
You're crazy, Snoink. But you look like you know what you're doing
Could I ask for some help? Algebra, first year university, second semester unit.
The last question of the assignment is ridiculous, as we haven't even gone over it in lectures, so I think it was meant to be a research question or something.
"Use Newton's Method to find the solutions of the equation xlnx = 6, correct to six decimal places.
and substituted a range of numbers (5 and 1 amongst them) into the formula from the wiki page (below), and kept on getting really varied answers that swung from -5 --> 8 -- > -104 and 7 --> -46 --> 7616. Just too varied and weird to keep on trying.
Don't you love it when teachers assign you calculus in an algebra class? XD
Also... attached! Download the PDF. Hopefully, it won't be confusing. If you have any questions, either PM me or post something on this thread. But make sure to say my name.
"The mark of your ignorance is the depth of your belief in injustice and tragedy. What the caterpillar calls the end of the world, the Master calls the butterfly." ~ Richard Bach
:/ Sorry, it's Algebra & Calculus MAB120, I didn't mean to sound as if I didn't know what I was doing I understood how to use Newton's Method, I just supplied it there for anyone who wanted to give it a shot.
Basically, that was the last question, so fair enough it'd be hard.
I know you used a calculator to differentiate xlnx - 6, but... When I differentiate that in my head, the first x turns into 1, the ln(x) becomes 1/x (as per log rules), and the 6 becomes nothing.
So:
f(x) = xln(x) - 6 f'(x) = 1/x
I'm so confused, you got: 1 + ln(x)...
Waaaaaaaaaait...
*slaps forehead*
Product rule, right?
u = x u' = 1 v = ln(x) v' = 1/x
dy/dx = u'v + v'u = 1ln(x) + x(1/x) = ln(x) + 1
*slaps forehead again*
I really need to remember that x, and ln or e^x are all separate functions, not just one when in a mash like 2xe^2x.
Aaaaanyway, yes, I can see that the rest of what you did is perfectly correct.
Thank you so much Did you do math at uni or something?
I'm a biochemical engineer, so I had to do calculus, differential equations (ordinary and partial), and linear algebra. So I like math!
Ubi caritas est vera, Deus ibi est.
"The mark of your ignorance is the depth of your belief in injustice and tragedy. What the caterpillar calls the end of the world, the Master calls the butterfly." ~ Richard Bach
Wow, a biochemical engineer sounds like hard work - where do you find the time to be a very active moderator on YWS?
Also, there was another question that I couldn't quite do, if you were bored and felt like some more math. No need for you to do it though, just thought I'd share.
"Find the equations to the tangents to the curve whose equation is y^3 + yx^2 + x^2 - 3y^2 = 0, at the points where y = 1."
As I saw no other way, I used implicit differentiation and wound up with a huge mess and an answer at the end I don't know what to do with :3
EDIT: Yeah Lava It's not a hard rule, it's just that when xlnx is there for me to see, I see it as one function, instead of the two that it is *shakes fist at person who created product rule*
You know that place between sleep and awake, that place where you still remember dreaming? That’s where I’ll always love you. That’s where I’ll be waiting. — J.M. Barrie, Peter Pan
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