First, the matching method

Applicable types: quadratic function and questions that can be transformed into quadratic function by method of substitution.

Example 1 Find the range of the function.

Solution: for the convenience of calculation, we might as well: the formula is,

Using the knowledge of quadratic function, we can get:

Example 2 Given the function y = (ex-a) 2+(e-x-a) 2 (a ∈ r, a≠0), find the minimum value of the function y. 。

Analysis: y = (ex-a) 2+(e-x-a) 2 = (ex+e-x) 2-2a (ex+e-x)+2a2.

Let t = ex+e-x and f (t) = t2-2at+2a2-2.

∵t≥2, ∴ f (t) = T2-2at+2a2-2 = (t-a) 2+a2-2 are defined as the maximum and minimum values in the upper domain, respectively.

Analysis: Because f'(x)= 3 x2-3, let f'(x)= 0, and get x =- 1 (positive).

F (-3) =- 17，F (- 1) = 3，F (0) = 1。 In contrast, the maximum value of f(x) is 3 and the minimum value is-17.