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What formula is used for the lowest point and symmetry axis of the general formula of quadratic function of one variable in mathematics?
The basic expression of unary quadratic function is:?

y=ax? +bx+c(a≠0)?

1. Symmetry axis formula: straight line x =-b/2a.

2. Lowest point:

(1) When a > 0, the parabola opens upward and has the lowest point, and the coordinates of the lowest point are (-b/2a, (4ac-b? )/4a)?

(2) When a < 0, the parabola opens downwards and has no lowest point.

Extended data:

Properties of quadratic function:

The image of 1. quadratic function is a parabola, but the 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 x =-b/2a. The only intersection of the symmetry axis and the parabola is the vertex p of the parabola. Especially when b = 0, the symmetry axis of parabola is Y axis (that is, straight line x = 0).

2. A parabola has a vertex p with coordinates p (-b/2a, (4ac-b? )/4a).

-b/2a = 0, p is on the y axis; When △ = b? At-4ac, p is on the x axis.

3. Quadratic coefficient A determines the opening direction and size of parabola.

When a > 0, the parabolic opening is upward; When a < 0, the parabolic opening is downward.

The larger a is, the smaller the opening of parabola is; The smaller a is, the larger the opening of parabola is.

4. Both the linear coefficient b and the quadratic coefficient a*** determine the position of the symmetry axis.

When the signs of A and B are the same (that is, AB > 0), the symmetry axis is on the left side of Y axis;

When the signs of A and B are different (that is, AB < 0), the symmetry axis is on the right side of the Y axis.

(Coincidentally, the left and right are different)

5. The constant term c determines the intersection of parabola and Y axis. The parabola intersects the Y axis at (0, c)

6. Number of intersections between parabola and X axis:

△ = B2-4ac > 0, and the parabola has two intersections with the X axis.

When △ = b2-4ac = 0, there are 1 intersections between the parabola and the X axis.

△ = B2-4ac < 0, and the parabola has no intersection with the x axis.

7. When a > 0, the function obtains the minimum value f (-b/2a) = (4ac-b? )/4a;

The function is decreasing at (-∞, -b/2a,+∞) and increasing function at -b/2a; The opening of parabola is upward; The range of the function is (4ac-b? )/4a,+∞).

When a < 0, the function obtains the maximum value f (-b/2a) = (4ac-b? )/4a;

The function is a increasing function at (-∞, -b/2a,+∞) and a decreasing function at -b/2a; The opening of parabola is downward; The range of the function is (-∞, (4ac-b? )/4a .

When b = 0, the axis of symmetry of parabola is the Y axis. At this point, the function is even, and the analytic expression is transformed into y=ax2+c(a≠0).

8. domain: r

Scope: When a>0, the scope is (4ac-b? )/4a,+∞); When a<0, the range is (-∞, (4ac-b? )/4a .

Parity: when b=0, this function is even; When b is not equal to 0, this function is a parity function.

Periodicity: None

Resources: Baidu Encyclopedia _ Quadratic Function