When a is less than 0, the opening is downward and the function has a maximum value. Vertex coordinates are (-2a-b, 4a-4ac-b squared), which means that a, b and c are substituted into them respectively to get vertex coordinates. 4A-4ac-b squared is the maximum.
Extended data:
Generally speaking, a function with the shape (a, b and c are constants) is called a quadratic function, where a is called a quadratic term coefficient, b is a linear term coefficient and c is a constant term. X is the independent variable and y is the dependent variable. The maximum number of independent variables to the right of the equal sign is 2.
Vertex coordinates? The intersection point is (only parabola with intersection point with X axis), and the coordinates of intersection point with X axis are sum.
Note: "Variable" is different from "unknown", so it cannot be said that "quadratic function means that the polynomial function with the highest number of unknowns is quadratic". "Unknown" is just a number (the specific value is unknown, but only one value is taken), and "variable" can take any value within a certain range.
The concept of "unknown" is applied in the equation (both functional equation and differential equation are unknown functions, but both unknown and unknown functions generally represent a number or function-special circumstances may occur), but the letters in the function represent variables and their meanings have always been different. From the definition of function, we can also see the difference between them.
References:
Baidu Encyclopedia-Quadratic Function