How do you find the formula for a quadratic equation?

I know how do to do linear equations and how to figure out the equation when you have two points.

But how do you know what the formula for a quadratic equation?

For example: If I graphed this -

how would I find its formula? I do not seek an answer, I want to know how you arrive at that answer.

y=mx.c

Or atlest that's what I think.

y = ax2 + bx +c

xv = -b/2a
yv = -(b2 - 4ac)/4a

v = vertix (in your pics case xv = yv = 0)

NOw, for every (x,y) you have, you throw it in the y = ... equation to find a, b and c

Then you will get the whole y = ... eqaution which is the formula of that parabole (I don´t the name in english - that shape)

So you do you want to show how to use it with the graph I presented as an example?

That's for lineal equations

That's right, but here's the easier form

a= (y-yv) / (x-xv)^2

b= - 2a * xv

c= yv + a * xv^2

(-2,4)
(2,4)
(1,1)
(-1,1)
(0,0)

A lot of points. Too easy.

y = ax2 + bx +c

(0,0) -> 0 = a02 + b0 +c --> c = 0

(1,1) -> 1 = a12 + b1 +0 --> a + b = 1 (A)

(-1,1) -> 1 = a(-1)2 + b(-1) + 0 --> a - b = 1 (B)

A + B = 2a = 2 --> a=1

A = a + b = 1 --> 1 +b = 1 --> b=0

Final equation --> y = x2

Maybe you are right, but I have been doing t my way for so long that your way seems weird to me. So, I will stick to mine, thank you very mcuh.

y=a (x-h)^2+k

So the vertex is the point where the parabola becomes symmetrical over the x-axis?

 y = x^2

I cant tell just by looking at it.

People here can give you forumuals to find it out, but you really need to be able to look at a graph and logically figure out what it is.  For instance, Y is always positive but X is positive and negative, so y has an odd power and x has an even power.  X increases at a faster rate than Y so X has a higher power.  From there you can just start plugging points into an quadratic equation to get the answer.

If the graphs moves from the origin, just add or subtract from the equation.  Say this same equation was moved rup 1 unit, then you could deduce the equation the same as above, then ask yourself what would need to happen for the graph to move.  If it was y = x^2 +1, then at x=0 y=1,  at x=1 y = 2, and so forth.