Note: When the coefficient of quadratic term is positive, there is no maximum value. There is no maximum because the opening is upward at this time.

The image of quadratic function is a parabola, but parabola is not necessarily a quadratic function. The parabola of the opening up or down is a quadratic function. Parabola is an axisymmetric figure.

The symmetry axis is a straight line, and the only intersection point between the symmetry axis and the parabola is the vertex p of the parabola. Especially when b=0, the symmetry axis of the parabola is the Y axis (that is, the straight line x=0).

main feature

"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, just as function is not equal to function relationship.

The situation of quadratic function image intersecting with x axis

When △=b? -4ac & gt； 0, the function image has two intersections with the x axis.

When △=b? When -4ac=0, the function image has only one intersection with the x axis.

When △=b? -4ac & lt； 0, the function image does not intersect with the x axis.