Linear function: what is it like? y=kx+b？ (k is an arbitrary constant other than 0 and b is an arbitrary constant) is called a linear function (linear? Function), also known as linear function, whose image can be represented by a straight line in a plane rectangular coordinate system. When the value of one variable in a linear function is determined, the value of another variable can be determined by a linear equation.
Quadratic function:
Generally, the function in the form of y = ax 2+bx+c is called quadratic function (quadratic? Function). Quadratic function is a polynomial function whose independent variable has the highest quadratic degree.
Quadratic function image
The image is a parabola in a plane rectangular coordinate system.
Symmetry axis and vertex coordinates
The symmetry axis of the quadratic function y = a (x-h) 2+k is x=h, and the vertex coordinates are (h, k).
Generally speaking, we can find the parabola y = ax 2+bx+c by matching method. Vertex and symmetry axis of (a≠0).
y=ax^2+bx+c
=a(x+b/2a)^2+(4ac-b^2)/4a
So, what is the symmetry axis of parabola y = ax 2+bx+c? X=-(b/2a), what is the vertex coordinate? (-(b/2a),(4ac-b^2)/4a)
Cubic function: what is it like? y=ax^3+bx^2+cx+d？ A function (a ≠ 0, b, c and d are constants) is called a cubic function (cubes? Function). The image of cubic function is a curve-regression parabola (different from ordinary parabola), which has special properties.
Other special polynomial functions
The special forms of polynomial function include not only linear function, quadratic function and cubic function, but also quartic function and quintic function.