Question

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

Answer 1

this one?

Answer 2

It's one of three my friend! lol.

Answer 3

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").

Answer 4

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

Answer 5

lol....ok

Answer 6

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?

Answer 7

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.

Answer 8

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

Answer 9

So that would be the uncommon example?

Answer 10

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

Answer 11

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.

Answer 12

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...

Answer 13

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?

Answer 14

SO that problem has two roots?

Answer 15

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..

Answer 16

Lol....wow.

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

3?

Answer 21

3 numbers.....yeah

Answer 22

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

Answer 23

7, 3, 35

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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.

Answer 28

Dear God my brain hurts.

Answer 29

Any useful examples to share?

Answer 30

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

Answer 31

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 :)

Answer 32

An arch of throwing a baseball?

Answer 33

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

Answer 34

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

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

this is the pyth thrm....

Answer 39

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

Answer 40

a^2 + b^2 = c^2

Answer 41

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

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

it can even be expanded to:

c^2 = a^2 + b^2 -2ab cos(C)

Answer 48

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

Answer 49

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 :)

Answer 50

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

Answer 51

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

Answer 52

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?

Answer 53

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

Answer 54

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.....

Answer 55

the steps I use are:

1) look at the problem
2) factor as needed
3) write down the answer
4) go to next problem?

Answer 56

factor left side? does that make sense?

Answer 57

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

Answer 58

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

Answer 59

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

Answer 60

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.

Answer 61

4) Go to the next problem? HA!

Answer 62

:) 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

Answer 63

Can any be elimianted?

Answer 64

OIC.

Answer 65

*eliminated

Answer 66

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

Answer 67

Could the steps be rearranged?

Answer 68

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.

Answer 69

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. :)

Answer 70

Ciao bella :)

Answer 71

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

Answer 72

..works for me :)