Definition and expression of quadratic function Generally speaking, there is the following relationship between independent variable X and dependent variable Y: Y = AX 2+BX+C.
(a, b, c are constants, a≠0, a determines the opening direction of the function, a >；; 0, the opening direction is upward, a
The right side of a quadratic function expression is usually a quadratic trinomial.
Quadratic function and unary quadratic equation, especially quadratic function (hereinafter referred to as function) y = ax 2+bx+c,
When y=0, the quadratic function is a univariate quadratic equation about X (hereinafter referred to as equation), that is, AX 2+BX+C = 0.
At this point, whether the function image intersects with the X axis means whether the equation has real roots. The abscissa of the intersection of the function and the x axis is the root of the equation.
Methods of solving high scores of quadratic function in junior middle school: complement method and cut method
Commonly used processing methods in geometric figures include division and shape filling. The key point of this method is to supplement or cut the area of the figure appropriately, so as to make it a figure which is beneficial to express the area.
Radial
Mainly refers to the image transformation with the vertex of quadratic function image as the rotation center and the rotation angle of180. This rotation will not change the image shape of the quadratic function, and the opening direction is opposite, so the value of a will be the original reciprocal, but the vertex coordinates will remain unchanged, so it is easy to find its analytical formula.
Axial symmetry
This graphic transformation includes two ways: X-axis symmetry and Y-axis symmetry.
The image of a quadratic function is symmetrical about X axis, but its shape remains the same, but the direction of opening is opposite, so the value of a is the original reciprocal. When the vertex position changes, as long as the new vertex coordinates are obtained according to the coordinate characteristics of the point symmetrical about the X axis, the analytical formula can be determined.
The quadratic function image is symmetrical about Y axis, and its shape and opening direction remain unchanged, so the value of A remains unchanged. However, the position of the vertex will change. As long as the new vertex coordinates are obtained according to the coordinate characteristics of the points symmetrical about the Y axis, the analytical formula can be determined.