What is the principle of quadratic functions? What is a quadratic function?

The basic oak representation of the quadratic function is y=ax +bx+c(a≠0). The quadratic function must be quadratic at its highest order, and the image of the quadratic function is a parabola whose axis of symmetry is parallel to or coincides with the y-axis.

The quadratic function expression is y=ax +bx+c (and a≠0) and is defined as a quadratic polynomial (or monomial).

If the value of y is equal to zero, a quadratic equation is obtained. The solution of this equation is called the root of the equation or the zero point of the function.

A quadratic function is an equation in which there are two unknowns, and there is only one unknown with a maximum order of two.

In general, a function of the form y=ax hidden land segment + bx+c(a≠0) (a, b, c are constants) is called a quadratic function, where zao yu a is the secondary term coefficient of the second sizhou, b is the primary term coefficient, c is the constant term, x is the independent variable, and y is the dependent variable.

A quadratic function, also known as a unary quadratic function, is a function of the form y=ax 2+bx+c, where a, b, c are arbitrary real numbers and a≠0.

A quadratic function describes a curve on a planar Cartesian coordinate system. where a is the quadratic coefficient, which determines the sum of the opening directions of the curve"Steepness"；b is the primary term coefficient, which determines the position of the curve on the coordinate system; c is a constant term that determines the intercept of the curve from the y-axis.

The image of a quadratic function can be a parabola with an opening up or down, or a straight line parallel to the x-axis, or a single point. The exact image shape and position are determined by the values a, b, and c in the function.

For the quadratic function y = ax 2 + bx + c, its image goes through the following steps:

1.If a>0, the curve opening is up; If a<0, the curve opens the hand downward.

2.When a≠0, the axis of symmetry of the curve is x=-b 2a.

3.If b>0, the curve is upward on the left side of the axis of symmetry; If b<0, the curve is up to the right of the axis of symmetry. If the line x=-b 2a intersects the y-axis, then this point is the vertex of the curve.

4.When c>0, the intersection of the curve with the y-axis is above the y-axis; When c<0, the intersection of the curve with the y-axis is below the y-axis. If c=0, then the curve intersects the y-axis at the origin.

Characteristics and properties of quadratic functions:

1.If a>0, the minimum value of the quadratic function is c-b 2 4a; If a<0, the maximum value of the quadratic function is also c-b 2 4a.

2.When a>0, the function approaches positive infinity when x approaches positive infinity or negative infinity. When a<0, the function approaches negative infinity when x approaches positive infinity or negative infinity.

3.If a>0, the number of intersections between the curve and the x-axis is zero or two; If a<0, the number of intersections between the pickpocketing curve and the x-axis is zero or two.

4.When a>0, the curve is the minimum at the vertices; When a<0, the curve is the maximum at the vertices.

5.When a>0, the function has monotonically increasing intervals of (-b 2a) and (b 2a, and the function has monotonically decreasing intervals of (-b 2a, b 2a). When a<0, the function monotonically decreases between (-b 2a) and (b 2a), and the function monotonically increases between (-b 2a, b 2a).

6.When a≠0, the axis of symmetry of the curve is x=-b 2a.

Question 1: What is b-4ac in a quadratic function??? If b2-4ac 0, the function has two intersections with the x-axis.

If b2-4ac=0, the function has an intersection point with the x-axis. If b2-4ac 0, function 1 has no intersection with the x-axis.

Question 2: What is the fixed point of a quadratic function? I haven't heard of a fixed point, but hand luck is what you said about a fixed point, which should refer to a certain fixed point, right? It's a quadratic function, and no matter how the coefficients change, the function always passes a fixed point, and you can find the coordinates of that fixed point.

For example, the function y=ax2+bx+3 (the function always crosses (0,3) points, regardless of the value of a b).

Question 3: What do quadratic functions a, b, and c represent 5 points Conceptually, a is called the quadratic coefficient (note that in the binary function, a is not equal to 0), b is called the primary coefficient, and c is called a constant.

From the perspective of the image of the quadratic function, the meaning of a is important, when a > 0, the image opening is upward; When a

A quadratic function is a function of the following form: y = ax 2 + bx + c, where a, b, and c are constants, circular difference, and a is not equal to zero. An image of a quadratic function usually presents a smooth arc, called a parabola.

The properties of quadratic functions are as follows:

1.Symmetry: The image of a quadratic function is symmetrical with respect to the straight line x = b (2a) in the vertical direction. That is, for a given quadratic function image, the points on the left and right sides of that line have exactly the same value of y.

2.Opening Direction: The opening direction of a quadratic function is determined by the positive or negative of a. When A is greater than zero, the parabolic opening is upward; When a is less than zero, the parabolic opening is downward.

3.Zero and axisymmetric points: The zero point of the quadratic function is the x value such that y is equal to zero, which can be obtained by solving the equation ax 2 + bx + c = 0. The axisymmetric point is the vertex of the parabola, and its x-coordinate is one-half of the -x-coordinate.

4.Maximum: When the parabolic opening is upward, the minimum value of the quadratic function occurs at the axisymmetric point; When the parabolic opening is downward, the maximum value of the quadratic function occurs at the axisymmetric point.

5.Incrementality: When a is greater than zero, the value of the quadratic function gradually increases as x increases; When a is less than zero, the value of the quadratic function gradually decreases as x increases.

6.Range: The range of the quadratic function depends on the opening direction. When the parabola opening is upward, the range is all positive real numbers; When the parabolic opening is downward, the range is all negative real numbers.

To sum up, the image of the quadratic deficit function is a smooth parabola with properties such as symmetry, opening direction, zero and axisymmetric points, maximum value points, increase and decrease, and range. These properties have important application value in solving mathematical problems, analyzing curve trends and trends.

1) General formula: y ax2+bx+c (a, b, c are constants, a≠0), then y is called a quadratic function of x. Vertex coordinates (-b 2a, (4ac-b 2) 4a).

2) Vertex formula: y a(x-h)2+k or y=a(x+m) 2+k(a,h,k is constant, a≠0)

3) Intersection type (with x-axis): y=a(x-x1)(x-x2) (also called two-point type, two-root type, etc.).

General. y ax2+bx+c (a,b,c is constant, a≠0), then y is called a quadratic function of x. Vertex coordinates (-b 2a, (4ac-b 2) 4a).

Vertex style. y a(x-h)2+k or y=a(x+m) 2+k(a,h,k is constant, a≠0)

3.Intersection (and x-axis): y=a(x-x1)(x-x2) (also called two-point, two-root, etc.).