Quadratic function symmetry axis formula: x=-b/2a. The basic expression of quadratic function is y = a (the square of x) +bx+c(a is not equal to 0). The highest order of a quadratic function must be quadratic, and the image of a quadratic function is a parabola whose symmetry axis is parallel or coincident with the Y axis.
The expression of quadratic function is y = a (the square of x) +bx+c(a is not equal to 0), which is defined as quadratic polynomial (or monomial).
If the value of y is equal to zero, a quadratic equation can be obtained. The solution of this equation is called the root of the equation or the zero of the function.
History of quadratic function:
Around 480 BC, Babylonians and China had found the positive root of quadratic equation by collocation method, but did not put forward the general solution. Around 300 BC, Euclid proposed a more abstract geometric method to solve quadratic equations.
In the 7th century, Brahmagupta of India was the first person who knew how to use algebraic equations, which allowed positive and negative roots.
In 1 1 century, Elazemi of Arabia independently developed a set of formulas for finding positive solutions of equations. Abraham Bachyat (also known as the Latin name Sawasoda) introduced the complete solution of the quadratic equation of one variable to Europe for the first time in his book Liber embadorum.
It is said that Schridde Haller was one of the first mathematicians to give the general solution of quadratic equation. But this was controversial in his time. The solution rule is: both sides of the equation are multiplied by the coefficient of unknown quadratic term four times at the same time; At the same time, the square of the coefficient of the unknown term is added to both sides of the equation; Then open the second square on both sides of the equation at the same time (quoted from Poshgaro II).