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It's one of three my friend! lol.
an uncommon example eh..... the quadratic formula is derived from a method know as "completing the square"; and is used to find the real roots of a quadratic expression (quadratic just being a fancy name for "squared").
there are 2 named parts to the quadratic formula that I tend to get backwards; the determinate and the discriminate..they were haveing a sale on "d" words back then and so were stuck with them
the discriminte, if it so be called, is the part -b/2a and it gives you the axis of symmetry of the parabola.... to find the vertex, the hoghest or lowest point of the parabola; we use the vertex in the equation to come up with the "y" part...make sense so far?
the other "d" word, the determinate perhaps, is a square root portion of the quad formula and it tells us whether there is: no roots, 1 root, or 2 roots.
ummmm........clear as mud. But it's mainly me.
So that would be the uncommon example?
dunno about any "uncommon" examples really, still trying to figure out what that means... maybe its talking about a quadratic that aint easily factored.....
if the square root portion has under its radical umbrella a negative #, there are no real roots; if it equals zero, then there is only 1 root, and if it is greater than zero, there are going to be 2 roots.
the quad formula is: -b sqrt(b^2 - 4ac) ---- +- ------------- 2a 2a here you can see the two parts :) i shoulda prolly put that up first...
No just an everyday example that might not be the first one you think of. Like, doesn't airplanes have something to do with the quadratic formula?
SO that problem has two roots?
that is not a problem ; that is the formula to determine the roots :) the standard quadratic equation is of the form: ax^2 +bx +c where a.b.and c are numbers...coefficients..
depending on the values of a,b,and c we can use the quadratic formula to determine its axis of symmetry, vertex coordinates, and all known solutions to y=0
lets try to make up an equation and test the quad formula out.... and try to stay away from airplanes :)
what are your favorite three numbers in the whole wide world... :)
Oh wait.......it said provide a USEFUL example..... duh. Not uncommon, or whatever I wrote.
7, 3, 35
ok..7 3 and 35; lets put them into the hat....stir it up...and pick one...............3 ok, a = 3; try again................7; b = 7 .......and stir again for effect........we get a 35; c = 35
3x^2 +7x -35...thats a quadratic formula...is it useful? dunno. but lets try out our formula.
the first thing we should do is see if its worth trying to find any roots: sqrt((7)^2 - (4)(3)(-35)) if this is zero or above, were good to go. sqrt(49 + 420) = sqrt(469) its a keeper so that last part is gonna be: +- sqrt(469)/2(3) the axis of symmetry is gonna be: -b/2a = -7/2(3) = -7/6
so we have a center for our parabola, its at x = -7/6 if we add and subtract the other part from this, we will know our solutions.
Dear God my brain hurts.
Any useful examples to share?
(-7/6) + sqrt(469)/6 = about 2.4427
this might be useful :) one example is the arch formed by throwing a baseball to your son.... you can determine its position with a quadratic equation.... but the "roots" of it are not that exciting :)
An arch of throwing a baseball?
the other root we got is about: -4.7761 you never seen a person throw a baseball around? it tends to go up, then comes back down into the golve of the oter person. makes for a nice arch while it flys thru the air
Yeah! Gotcha! Now......what do you know about Pythogorean Therorem's......or whatever it is?
i know that guy was a nutjob..... but his theorum is pretty helpful :)
So was Pavlov. Ok......one sec...
There are many applications for the Pythagorean Theorem.. can you give a specific example and show with calculations how the Pythagoras theorem applies?
the square of the sum of the legs of a right trianlge are equal to the square of the hypotenuse side.
a^2 + b^2 = c^2
OH.....and one more on quadratics too..
Nice attachment, am I supposed to color it? JK!
lol..... use it as a place mat ;)
So that a^2 thing is the formula for that>?
it is.... the names of the variables are unimportant, but that is a common rendition of it. another one is: x^2 + y^2 = r^2 and another one is: sin^2 + cos^2 = 1
all for the sum of the legs of a right triangle?
it can even be expanded to: c^2 = a^2 + b^2 -2ab cos(C)
yep, since right triangle are about the easiest to use; its nice to have stuff you can use with them :)
since the cos(90) = 0, that last part vanishes in the right trianlge and your left with the sum of the squares of the sides :)
Ok......one more the quadratics thing.....
ok....... I hope your writeing this stuff down :) I might forget it all by tomorrow :)
Explain the four-steps for solving quadratic equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand?
No kidding.......writing away!
ive seen this one before in here and it seems to be an odd question in general. the four steps? they might be talking about the 4 common ways that quads are facttored, but then it says to elinate one of them as tho they were all used together.....
the steps I use are: 1) look at the problem 2) factor as needed 3) write down the answer 4) go to next problem?
factor left side? does that make sense?
doesnt clarify my quandry.....no.....
id have to look up and google it to see what its talking about to give a good answer
Maybe something like this: Step 1: Find two numbers that add together to get the middle term, and multiply to get the last term. Step 2: Rewrite the equation with those numbers: Step 3: Factor the first two and last two terms separately: Step 4: If you've done this correctly, your two new terms should have a clearly visible common factor.
4) Go to the next problem? HA!
:) yeah. there are many techniques used to factor, I have my favorites, but really, the steps you are looking for will be defined by the source you are using
Can any be elimianted?
im gonna go with a no on that one....eliminating steps just sounds bad...and Ive built alot of stairs in my day :)
Could the steps be rearranged?
gonna have to go with a no again for that one, the steps tend to be in order of what you do to get to the next one.....still sounds like a bad idea to be rearranging them.
Lol, ok....well you have been an AWESOME help up until this question anyway! Thanks so much. My brain is cramping up at this point. :)
Ciao bella :)
Lol, I may just write down "it sounds like a bad idea to me" just to see what kind of feedback i get!.
..works for me :)