The key to solve the vertex of quadratic function is to transform the general form into the vertex form. By collocation method, we can transform the general quadratic function into the vertex form: y = a (x-h) 2+k, where h and k are the abscissa and ordinate of the vertex respectively.
The conversion process is as follows:
1. Add the square of the general form of the quadratic function and half of the coefficient b of the linear term (that is, (b/2a) 2) to both sides of the equation to complete the formula of the square term.
2. Comparing the quadratic function with the vertex form Y = A (X-H) 2+K, we can get the abscissa h and ordinate k of the vertex.
The specific formula is as follows:
h=-b/(2a)k=4ac-b^2/(4a)
Through the above formula, we can get the vertex coordinates of the quadratic function. It should be noted that in the process of solving, a≠0 must be guaranteed, otherwise the equation will no longer be a quadratic function.
Taking a specific quadratic function as an example, such as y = x 2-3x+2, we can solve the vertex according to the following steps:
1. formula equation Y = X 2-3x+2: Y = (X 3/2) 2- 1/4.
2. Comparing the formula with the vertex form Y = a (x-h) 2+k, we can get: h =-(-3)/(2 *1) = 3/2k = 4 *1* 2-(-3) 2/(4 *).
So the vertex coordinates of this quadratic function are (3/2,-1/4).
Through the above method, we can solve the vertex coordinates of any quadratic function. In practical application, mastering the formula and method of solving the vertex of quadratic function is helpful for us to better analyze the properties of parabola and solve problems. In addition, vertex coordinates can also be used to solve the maximum value, symmetry axis and other information, which lays the foundation for subsequent mathematical analysis and problem solving.