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How to judge the functional relationship in math problems
You mainly mean quadratic function, right?

(1) general formula: y = ax 2+bx+c (a, b, c are constants, a≠0).

(2) Vertex: y = a(x-h)2+k[ vertex p (h, k) of parabola]

For the quadratic function y = ax 2+bx+c, its vertex coordinates are (-b/2a, (4ac-b 2)/4a).

(3) Intersection point: y = a (x-x1; )(x-x2)

[Only applicable to parabolas with intersections A(x 1 0) and B(x2, 0) with the X axis]

Where x 1, 2 =-b √ b 2-4ac.

When analyzing the formula, the parameters are determined mainly by solving the equation.