The analytical formula is 1. General formula: y = ax 2+bx+c (a, b and c are constants, and a≠0).
2. Vertex: y=a(x-h) 2 +k(a, h, k are constants, a≠0).
3. Two formulas: y = a (x-X 1) (x-x 2), where x1and x 2 are the abscissa of the intersection of parabola and X axis.
That is, the two roots of the unary quadratic equation ax 2+bx+c = 0, a≠0.
The concept of quadratic function is generally shaped like y=ax? The function of +bx+c(a, b, c are constants, and a≠0) is called quadratic function. What needs to be emphasized here is that, similar to the unary quadratic equation, the quadratic term coefficient a≠0, while b and c can be zero. The domains of quadratic functions are all real numbers. Quadratic function has two structural characteristics. The first one: the function on the left of the equal sign, the quadratic form on the right of the independent variable X, and the highest degree of X is 2. The second one: A, B, C are constants, A is a quadratic term coefficient, B is a linear term coefficient, and C is a constant term.
The property of quadratic function is 1. A quadratic function is a parabola, but a parabola is not necessarily a quadratic function. The parabola of the opening up or down is a quadratic function. Parabola is an axisymmetric figure.
2. A parabola has a vertex p whose coordinates are P(-b/2a, (4ac-b 2 )/4a). -b/2a=0, p is on the y axis; When δ = b 2-4ac = 0, p is on the x axis.
3. Quadratic coefficient A determines the opening direction and size of parabola. When a>0, the parabola opens upwards; When a<0, the parabola opens downward. The larger the |a|, the smaller the opening of the parabola.
The above is my knowledge about quadratic function, I hope it will help you.