Quadratic function drawing should consider vertex, opening direction, symmetry axis, zero point on X axis (let y=0 correspond to X value) and intercept on Y axis. Quadratic function is an axisymmetric figure, so it is more smooth to draw points by using this characteristic.
The graphs of inverse proportional function and quadratic function are convex (related to the second derivative).
Increase or decrease of functions:
When k>0, the image is located in the first quadrant and the third quadrant respectively. In the same quadrant, Y decreases with the increase of X..
When k < 0, the image is located in the second and fourth quadrants respectively, and in the same quadrant, y increases with the increase of x.
Nature:
(1) Any point on the inverse proportional function is equal to the area of the right triangle surrounded by the |k|/2 axis.
(2) The area of the triangle formed by any two points on the image and the origin is equal to the area of the right-angled trapezoid.
(3) When the inverse proportional function intersects the linear function, there is a relationship that the line segments are equal and the coordinate points are symmetrical about the origin.
(4) When the inverse proportion intersects the linear function, the coordinates of the intersection point can be found at the same time (the quadratic equation of one variable can be found at the same time to reflect the number of roots of the equation).