What is the quadratic formula? What is it used for? Give an uncommon example.

- anonymous

What is the quadratic formula? What is it used for? Give an uncommon example.

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- amistre64

this one?

- anonymous

It's one of three my friend! lol.

- amistre64

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").

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- amistre64

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

- anonymous

lol....ok

- amistre64

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?

- amistre64

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.

- anonymous

ummmm........clear as mud. But it's mainly me.

- anonymous

So that would be the uncommon example?

- amistre64

dunno about any "uncommon" examples really, still trying to figure out what that means... maybe its talking about a quadratic that aint easily factored.....

- amistre64

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.

- amistre64

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...

- anonymous

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?

- anonymous

SO that problem has two roots?

- amistre64

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..

- anonymous

Lol....wow.

- amistre64

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

- amistre64

lets try to make up an equation and test the quad formula out.... and try to stay away from airplanes :)

- amistre64

what are your favorite three numbers in the whole wide world... :)

- anonymous

3?

- amistre64

3 numbers.....yeah

- anonymous

Oh wait.......it said provide a USEFUL example..... duh.
Not uncommon, or whatever I wrote.

- anonymous

7, 3, 35

- amistre64

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

- amistre64

3x^2 +7x -35...thats a quadratic formula...is it useful? dunno. but lets try out our formula.

- amistre64

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

- amistre64

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.

- anonymous

Dear God my brain hurts.

- anonymous

Any useful examples to share?

- amistre64

(-7/6) + sqrt(469)/6 = about 2.4427

- amistre64

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 :)

- anonymous

An arch of throwing a baseball?

- amistre64

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

- anonymous

Yeah! Gotcha! Now......what do you know about Pythogorean Therorem's......or whatever it is?

- amistre64

i know that guy was a nutjob..... but his theorum is pretty helpful :)

- anonymous

So was Pavlov. Ok......one sec...

- anonymous

There are many applications for the Pythagorean Theorem.. can you give a specific example and show with calculations how the Pythagoras theorem applies?

- amistre64

this is the pyth thrm....

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- amistre64

the square of the sum of the legs of a right trianlge are equal to the square of the hypotenuse side.

- amistre64

a^2 + b^2 = c^2

- anonymous

OH.....and one more on quadratics too..

- anonymous

Nice attachment, am I supposed to color it? JK!

- amistre64

lol..... use it as a place mat ;)

- anonymous

So that a^2 thing is the formula for that>?

- amistre64

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

- anonymous

all for the sum of the legs of a right triangle?

- amistre64

it can even be expanded to:
c^2 = a^2 + b^2 -2ab cos(C)

- amistre64

yep, since right triangle are about the easiest to use; its nice to have stuff you can use with them :)

- amistre64

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 :)

- anonymous

Ok......one more the quadratics thing.....

- amistre64

ok....... I hope your writeing this stuff down :) I might forget it all by tomorrow :)

- anonymous

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?

- anonymous

No kidding.......writing away!

- amistre64

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.....

- amistre64

the steps I use are:
1) look at the problem
2) factor as needed
3) write down the answer
4) go to next problem?

- anonymous

factor left side? does that make sense?

- amistre64

doesnt clarify my quandry.....no.....

- amistre64

id have to look up and google it to see what its talking about to give a good answer

- anonymous

Hmmm..........ok.

- amistre64

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.

- anonymous

4) Go to the next problem? HA!

- amistre64

:) 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

- anonymous

Can any be elimianted?

- anonymous

OIC.

- anonymous

*eliminated

- amistre64

im gonna go with a no on that one....eliminating steps just sounds bad...and Ive built alot of stairs in my day :)

- anonymous

Could the steps be rearranged?

- amistre64

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.

- anonymous

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. :)

- amistre64

Ciao bella :)

- anonymous

Lol, I may just write down "it sounds like a bad idea to me" just to see what kind of feedback i get!.

- amistre64

..works for me :)

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