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Parabolic index formula of turnover
General formula: y=aX2+bX+c(a, b and c are constants, and a≠0).

Vertex: y=a(X-h)2+k(a, h, k are constants, a≠0).

Intersection point (two formulas): y=a(x-x 1)(x-x2)(a≠0), where the parabola y=aX2+bX+c(a, b, c are constants, a≠0) and the coordinate of the intersection point of the x axis, namely the equation ax2.

Common ground:

① The origin is on a parabola, and the eccentricity e is 1.

② Symmetry axis is coordinate axis;

③ The directrix is perpendicular to the axis of symmetry, the vertical foot and the focus are symmetrical to the origin respectively, and their distance from the origin is equal to 1/4 of the absolute value of the first coefficient.

Difference:

① When the axis of symmetry is the X axis, the right end of the equation is 2px and the left end of the equation is y^2;; ; When the symmetry axis is the Y axis, the right end of the equation is 2py and the left end of the equation is x^2;; ;

(2) When the opening direction is the same as the positive semi-axis of X axis (or Y axis), the focus is on the positive semi-axis of X axis (Y axis), and the right end of the equation takes a positive sign; When the opening direction is the same as the negative semi-axis of X (or Y), the focus is on the negative semi-axis of X (or Y), and the right end of the equation takes a negative sign.