Joined: Sat Oct 16, 2004 11:13 pm Posts: 2948 Location: Caucusland
The apex? Don't you mean the vertex?
I don't understand what you're asking for. The formula is easy:
ax^2 + bx + c = f(x)
has first derivative
2ax + b = f ' (x)
Setting the first derivative to zero gives the points on the graph whose tangent line has slope zero, i.e. the "hills" and "crests" in layman's terms. A parabola, of course, as a unique such point, for
2ax + b = 0
solves to
x = -b/(2a)
To find the y-value of the vertex, run this value of x through the function, which you should have entered on Excel.
It's been a year for me, but the way I'd do it is the following:
Enter the coefficients for the parabola in separate cells. (Remember, Excel doesn't understand what you mean when you write in "x", only cells). For example, if you have the parabola y = 2x^2 + 3x + 4, enter in cell a1 the number 2, then cell b1 the number 3, then cell c1 the number 4, then, in a separate cell, say d1, enter in = -b1 / (2*a1). For evaluation, enter (in another separate cell, say e1) enter in a1*d1^2 + b1*d1 + c1 and you'll have your evaluation for the vertex, with the x-value in cell d1 and the y-value in cell e1.
If you want a specific formula for the y-value of the vertex, feed the x-value through the function:
y = f(-b/(2a)) = a*(-b/(2a))^2 + b* (-b/(2a)) + c
= ab^2/(4a^2) - b^2/(2a) + c
= (ab^2 - 2ab^2 + 4ca^2)/(4a^2)
= (4ac-b)/(4a)
with common denominators and cancellation.
_________________
Bob Knight wrote:
When my time on Earth is gone, and my activities here are passed, I want they bury me upside down so my critics can kiss my ass.
If necessity is the mother of invention Then I'd like to kill the guy who invented this The numbers come together in some kind of 3rd dimension A regular algebraic bliss. Let's start with something simple Like one and one ain't three And two plus two will never get you five There's fractions in my subtraction And X don't equal Y But my homework is bound to multiply
Math sucks (math sucks) Math sucks (math sucks) I'd like to burn this textbook, I hate this stuff so much! Math sucks (math sucks) Math sucks (math sucks) Sometimes I think that I don't know that much--But math sucks!
I got so bored with my homework I turned on the T.V. The beauty contest winners were all smiling through their teeth They asked the new Miss America "Hey babe, can you add up all those bucks?" She looked puzzled then just said, "Math Sucks!"
Math sucks (math sucks) Math sucks (math sucks) You don't even have to spell it, all you have to do is yell it Math sucks (math sucks) Math sucks (math sucks) Sometimes I think that I don't know that much--But math sucks!
Geometry, trigonometry, and if that don't tax your brain There are numbers to big to be named (too big to be named) Numerical precision is a science with a mission And I think it's gonna drive me insane
Parents fighting with their children and the Congress can't agree, Teachers and their students are all jousting constantly Management and labor keep rattling old sabers, Quacking like those Peabody ducks
Math sucks (quack quack) Math sucks (quack quack) You don't even have to spell it, all you have to do is yell it! Math sucks (math sucks) Math sucks (math sucks) Sometimes I think that I don't know that much--But math sucks!
Math sucks, math sucks, math sucks the big one Math sucks, math sucks, math sucks the big one
_________________ "A waffle is like a pancake with a syrup trap." - Mitch Hedberg
Joined: Sat Mar 04, 2006 11:46 pm Posts: 4970 Location: Portland, OR Gender: Male
Merrill wrote:
The apex? Don't you mean the vertex?
I don't understand what you're asking for. The formula is easy:
ax^2 + bx + c = f(x)
has first derivative
2ax + b = f ' (x)
Setting the first derivative to zero gives the points on the graph whose tangent line has slope zero, i.e. the "hills" and "crests" in layman's terms. A parabola, of course, as a unique such point, for
2ax + b = 0
solves to
x = -b/(2a)
To find the y-value of the vertex, run this value of x through the function, which you should have entered on Excel.
It's been a year for me, but the way I'd do it is the following:
Enter the coefficients for the parabola in separate cells. (Remember, Excel doesn't understand what you mean when you write in "x", only cells). For example, if you have the parabola y = 2x^2 + 3x + 4, enter in cell a1 the number 2, then cell b1 the number 3, then cell c1 the number 4, then, in a separate cell, say d1, enter in = -b1 / (2*a1). For evaluation, enter (in another separate cell, say e1) enter in a1*d1^2 + b1*d1 + c1 and you'll have your evaluation for the vertex, with the x-value in cell d1 and the y-value in cell e1.
If you want a specific formula for the y-value of the vertex, feed the x-value through the function:
y = f(-b/(2a)) = a*(-b/(2a))^2 + b* (-b/(2a)) + c
= ab^2/(4a^2) - b^2/(2a) + c
= (ab^2 - 2ab^2 + 4ca^2)/(4a^2)
= (4ac-b)/(4a)
with common denominators and cancellation.
Let me explain what this is for..
I have to find the optimum moisture and density of soil for use in compaction. I take five different samples of the same soil and add water to each in steadily higher incraments. I then take these soil samples and compact them in a machine. As the Moisture % increases with each point...the mass of the compacted soil also increases, but at at unknown point the mass begins to drop...this is the point at which the soil is at optimum moisture % for compaction. Since this may occur in between two of the samples that I have added water too...I can't nail down that optimum point without plotting all five points on a graph with an X and Y axis. I then connect the five dots and they form a parabolo. For years now I have been going to the top of the parabola and finding the optimum value manually by following in a straigh line from the top of the parabola to both the X and Y axis. I now have put all of this into excel...it calculates and plots everything for me, but I havn't been able to figure out how to get excel to find that "Optimum" point at the peak of the curve and place that value into a cell.
I'm not a math wiz...not even close really. So what you wrote above, while seeming easy to you...only makes me want to kill myself. I need to type a formula into a pre-selected cell that will find the peak of the curve (parabola). I'm sure the answer lies somewhere in that suicide inducing mess above
Can you simplify given the information I have given
Joined: Sat Oct 16, 2004 11:13 pm Posts: 2948 Location: Caucusland
porchball wrote:
Merrill wrote:
The apex? Don't you mean the vertex?
I don't understand what you're asking for. The formula is easy:
ax^2 + bx + c = f(x)
has first derivative
2ax + b = f ' (x)
Setting the first derivative to zero gives the points on the graph whose tangent line has slope zero, i.e. the "hills" and "crests" in layman's terms. A parabola, of course, as a unique such point, for
2ax + b = 0
solves to
x = -b/(2a)
To find the y-value of the vertex, run this value of x through the function, which you should have entered on Excel.
It's been a year for me, but the way I'd do it is the following:
Enter the coefficients for the parabola in separate cells. (Remember, Excel doesn't understand what you mean when you write in "x", only cells). For example, if you have the parabola y = 2x^2 + 3x + 4, enter in cell a1 the number 2, then cell b1 the number 3, then cell c1 the number 4, then, in a separate cell, say d1, enter in = -b1 / (2*a1). For evaluation, enter (in another separate cell, say e1) enter in a1*d1^2 + b1*d1 + c1 and you'll have your evaluation for the vertex, with the x-value in cell d1 and the y-value in cell e1.
If you want a specific formula for the y-value of the vertex, feed the x-value through the function:
y = f(-b/(2a)) = a*(-b/(2a))^2 + b* (-b/(2a)) + c
= ab^2/(4a^2) - b^2/(2a) + c
= (ab^2 - 2ab^2 + 4ca^2)/(4a^2)
= (4ac-b)/(4a)
with common denominators and cancellation.
Let me explain what this is for..
I have to find the optimum moisture and density of soil for use in compaction. I take five different samples of the same soil and add water to each in steadily higher incraments. I then take these soil samples and compact them in a machine. As the Moisture % increases with each point...the mass of the compacted soil also increases, but at at unknown point the mass begins to drop...this is the point at which the soil is at optimum moisture % for compaction. Since this may occur in between two of the samples that I have added water too...I can't nail down that optimum point without plotting all five points on a graph with an X and Y axis. I then connect the five dots and they form a parabolo. For years now I have been going to the top of the parabola and finding the optimum value manually by following in a straigh line from the top of the parabola to both the X and Y axis. I now have put all of this into excel...it calculates and plots everything for me, but I havn't been able to figure out how to get excel to find that "Optimum" point at the peak of the curve and place that value into a cell.
I'm not a math wiz...not even close really. So what you wrote above, while seeming easy to you...only makes me want to kill myself. I need to type a formula into a pre-selected cell that will find the peak of the curve (parabola). I'm sure the answer lies somewhere in that suicide inducing mess above
Can you simplify given the information I have given
I did, in the middle of the writing, point out how you can do it easily on Excel.
I'm supposing that your program gives you the parabola's equation. If not, you'll need to find a way to get the parabola's equation from the approximation; otherwise, you won't be able to use Excel.
There's probably an easier command, but this is definitely a way to do it:
Let's suppose y = -2x^2 + 3x + 4 is the estimated parabola for your data. This is a parabola that will yield a "maximum" point like your data above.
Now, go to Excel.
Enter in cell a1 the number "-2,"; likewise enter 3 in b1 and 4 in c1.
In cell d1, enter in the following code: " = b1 / (2*a1) ". You can do this by clicking on cell b1 and a1. Next to d1, label it "opt. moisture" or something that can remind you what's in d1.
In cell e1, enter in the following code " = a1*d1^2 + b1^d1 + c1". Next to this cell, call it "optimal mass."
You can put whatever coefficients your program estimates for your parabola in a1, b1, and c1, so this program is reusable. Remember, your parabola is a1 * x^2 + b1 * x + c1, so in our example, you would enter -2 for a1, 3 for b1, and 4 for c1. Note that you can just go in and change these data for whatever sample you're running once you get the estimated parabola for your data from your other program.
For our example, d1, your soil percentage, should read ".75" and your optimal soil mass in e1 should read "5.25."
Hope it works.
_________________
Bob Knight wrote:
When my time on Earth is gone, and my activities here are passed, I want they bury me upside down so my critics can kiss my ass.
Last edited by Merrill on Sun Oct 14, 2007 6:18 am, edited 2 times in total.
Joined: Sun Oct 17, 2004 4:43 pm Posts: 7633 Location: Philly Del Fia Gender: Female
I don't get it. how is it a math problem when there's no fucking numbers?! Seriously. All this A, B, Y bullshit kicks my dyslexia into full gear and my eyeballs start to projectile bleed like a cartoon.
Joined: Sat Oct 16, 2004 10:51 pm Posts: 14534 Location: Mesa,AZ
NaiveAndTrue wrote:
I don't get it. how is it a math problem when there's no fucking numbers?! Seriously. All this A, B, Y bullshit kicks my dyslexia into full gear and my eyeballs start to projectile bleed like a cartoon.
Wait till you see some of the problems on my old linear algebra tests.
_________________
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In my many years I have come to a conclusion that one useless man is a shame, two is a law firm, and three or more is a congress.
Joined: Mon Oct 18, 2004 9:10 am Posts: 17256 Location: Chichen to the Thing
NaiveAndTrue wrote:
I don't get it. how is it a math problem when there's no fucking numbers?! Seriously. All this A, B, Y bullshit kicks my dyslexia into full gear and my eyeballs start to projectile bleed like a cartoon.
wanna make out?
_________________ I'm like, OK, God, if there is an open door for me somewhere, this is what I always pray, I'm like, don't let me miss the open door
Joined: Sun Oct 17, 2004 4:43 pm Posts: 7633 Location: Philly Del Fia Gender: Female
bondcfh007 wrote:
NaiveAndTrue wrote:
I don't get it. how is it a math problem when there's no fucking numbers?! Seriously. All this A, B, Y bullshit kicks my dyslexia into full gear and my eyeballs start to projectile bleed like a cartoon.
wanna make out?
You ask me that a lot. I think we should just do it, get it out of the way. Do you live near Philly? Smoke? Eat lots of Garlic??
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that took me a minute...but seriously, can you find the apex of a parabola for me..that'd be great, and possibly save my ass tomorrow
