Can someone explain the concept of a quadratic equation?

So I'm doing math advancded placement and I'm on chapter 4 Quadratic and Polynomial Equation lesson 3 The Quadratic Formula. I know a quadratic equation is written in the form ax 2 + bx + c = 0. But thats pretty much it. Anyways if any one could explain...

the concept and maybe give a example or two that would be great

Quadratic equation is a squared plus b squared = c squared. It's used to find the lengh of three sides of a triangle.

The theory is the same as any other polynomial, and the Greeks found out that in a triangle, this formula holds true, irregardless of the varying types or lengths of the sides.

So by using the same method you use to solve a typical polynomial, you can solve this equation as well.

I haven't honestly seen the formula previously as you wrote it, though...and, to be honest, I took algebra (two years) trigonometry (one year) and pre-calculus (one year) so it could be that I didn't cover this aspect of the equation in question.

Er,

Actually, a squared plus b squared = c squared is the Pythagorean Theorem. And the proof only works to determine the length of the sides of a RIGHT triangle...

a squared plus bx plus c = 0 is a quadratic formula.

It's solved by using this formula:

x= -b +/- (square root (b2)) - 4AC

and then all divided by 2A.

It's said this way (if it helps)

X equals the opposite of B, plus or minus the square root of B squared minus 4AC, all divided by 2A.

Here's an example:

x² - 4x - 5 = 0

to solve, substitute it into the formula I gave you.

(I'll upload it as a picture)

simplify,

then X= 5 or -1.

I just looked it over and it looks SO complicated but it's not.

Check out this site to help you:
http://www.teacherschoice.com.au/Maths_Library/Algebra/Alg_6.htm

Well as long as you know the three methods to solve a quadratic equation, your good to go

the factor method [ the sum and product]
the d [ square method ]

say x square + 2x + 5 = 0

then a = 1 b = 2 c = 5

then you do this

b + or - root [ b square - 4 aXc ] divided by 2[a]

and the last one is completing the square method...

say you have x square + 4x + 5

you have to divide the coefficient of x by 2 and minus and plus the square of the answer you divided

Okay, hope that helps..I did this a long time ago!

there is a song that goes to it. and there is a way to prove the quadratic formula but that is precalc stuff which I am great in. I love math!!

ax2 + bx +c = 0 is just the general form of a quadratic. Every quadratic can be written in terms of this.

The purpose of a quadratic is that it is normally used to solve problems involving 2 unknown quantities that both can be written in terms of a common variable x.

E.g. If a rectangle has a length L = x+3 metres, a width W = x-1 metres and an area of 32 m squared. What is the width of the rectangle

Area = L * W
32 = (x+3)(x-1)
32 = x2 +2x -3
0 = x2 +2x -35
0 = (x+7)(x-5) [ Factorisation]
therefore x = -7 or x = 5 [ Solutions provided by zero factor theorem]

since we are talking about a dimension of a shape we cannot have a negative length, therefore x = 5 metres

and the width is 4 metres.

Hope this helped