First, solve the absolute value problem.
It mainly includes simplification, evaluation, equation, inequality, function and so on. The basic idea is to turn a problem with absolute value into a problem without absolute value. The specific transformation method is as follows:
1, classified discussion method: according to the positive, zero and negative scores of numbers or formulas in absolute value symbols, the absolute value is removed.
2. Zero-segment discussion method: it is suitable for the case that multiple absolute values contain one letter.
3. Bilateral flat method: it is suitable for equations or inequalities with non-negative edges.
4. Geometric meaning method: it is suitable for cases with obvious geometric meaning.
Second, algebraic evaluation.
The methods are: direct substitution, simplified substitution and appropriate deformation (sum product substitution). Note: When the algebraic expression evaluated is the letter "symmetry", it can usually be replaced by the letter "sum and product", so the evaluation can be replaced by "sum and product".
Third, solve the parameter equation.
Except for unknowns, other letters contained in the equation are called parameters, and this equation is called parametric equation. Generally, the method of classified discussion is adopted to solve the parametric equation, and its principle is: solve by type, discuss as needed, and write conclusions by classification.
Fourth, the solution of one-dimensional quadratic inequality
Factorization can be transformed into a set of binary linear inequalities to solve, but it is more complicated; Its simple and practical solution is to use the image of quadratic function to solve it according to the relationship between "three quadratic functions". The specific steps are as follows: make the second positive, judge the root, draw a schematic diagram and solve the set on the horizontal axis.