How to formulate the ordinary formula of the quadratic function into a vertex formula, such as y x 2

y=x^2-2x+2

x -2x)+2 puts the quadratic term together with the primary term, and the constant is left alone.

x -2x+1-1)+2 plus a 1, in order to match x -2x in a completely flat way, subtract a 1 to not change.

function, so pay attention to what number is added, while also subtracting the same number. Why.

Why do you want to add 1, how did you find this 1? Usually divide the coefficient of the primary term by 2 and then square it. As.

In this problem, the coefficient of the primary term is 2, and 2 2 = 1 ( 1) =1 So add 1, and for example, if x -3x is matched into a perfect flat method, how much should be added? The coefficient of the term is 3 , with.

3 2 = 3 2, (3 2) = 9 4 so add 9 4, but also subtract 9 4 so.

x²-3x+9/4 -9/4=（x-3/2)²-9/4

x-1)²-1+2

x-1)²+1

Another example: y=3x +4x+5

3 (x +4 3x+5 3) is different from the above: the coefficient of the quadratic term is not 1, so only 3 can be proposed, no.

If both sides are divided by 3 at the same time, then y will also be divided by 3 and it will become y 3.

3（x²+4/3x+4/9-4/9+5/3）

3[(x+⅔)11/9]

3(x+ )11 3 Finally remove the middle brackets and you're good to go!

I hope you can understand, if you don't understand, then look for me!

y=x 2 -2x-1=(x 2 -2x+1)-1-1=(x-1)Huzhou 2 -2, age pants cover.

Therefore, the pure implicit answer is y=(x-1) 2 -2

For example, the general form of a quadratic function: y = ax 2 + bx + c

After matching the vertex formula, it is: as in the letter y = a(x + b 2a) 2 + 4ac-b 2) 4a

The coordinates of the vertex guess oak are spike (-b 2a, (4ac-b 2) 4a).

Generally, the secondary or secondary function is y=ax +bx+c(a≠0)y=ax +bx+c=a[x +bx a+(b-parawood2a) c-(b 4a).

a[x+(b enlighten this 2a)] 4ac-b )4a vertex coordinates are (-b 2a, (4ac-b)4a).

y=ax +bx+c, which is converted into a vertex formula: y=a(x+b 2a) +4ac-b ) 4a The recipe process is as follows: y=ax +bx+c=a(x +bx a)+c=a(x +bx a+b 4a -b 4a)+c=a(x+b 2a) -b 4a+c=a(x+b 2a) +4ac-b ) 4a

On the image of a quadratic function:

Vertex formula: y=a(x-h) +k, the vertex coordinates of the parabola p(h,k): for the general quadratic function y=ax 2+bx+c its vertex coordinates are (-b 2a, (4ac-b) 4a).

If 2 of the 3 intersection points are the intersection points of the quadratic function and the x-axis, then the analytical formula of the quadratic function can be set as: y=a(x-x1)(x-x2) (x1,x2 is the coordinates of the 2 intersection points of the quadratic function and the x-axis), and the analytical formula of the quadratic function can be found according to the other point, if you know that the vertex coordinates are (h,k), then you can set the analytical formula of y=a(x-h)2+k, and the quadratic function analytic formula can be found according to another point.