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.