1. Determine the theme and content: Select a theme related to the quadratic equation of one variable, such as "Solution of the quadratic equation of one variable" and "Application of the quadratic equation of one variable". Then according to the theme and content, determine the central word or title of the mind map.
2. Layout: Draw a general layout on the paper, including prefix, primary branch, secondary branch, etc. It can be arranged in chapter order or knowledge point order. Draw first-level branches: Draw first-level branches according to the chapters or knowledge points in the textbook, such as "definition", "solution" and "application".
3. Draw secondary branches: Under the primary branches, draw secondary branches according to specific knowledge points or questions. For example, "solution" can include two levels of branching, such as "formula method", "factorization method" and "matching method"
There are several ways to solve a quadratic equation with one variable:
1. Factorization method: If the equation can be factorized into the product of two linear factors, then the solution of the equation can be obtained by setting each linear factor to zero respectively.
2. Complete square formula method: For a quadratic trinomial formula, it can be expressed as a square term plus a constant term, and then the standard form of the equation can be found and solved.
3. Matching method: When factorization cannot be directly used, the quadratic equation of one variable can be transformed into a completely flat way or the primary term can be removed by matching method. Usually, the matching method needs some algebraic deformation to achieve the goal.
4. Formula method: Use the root formula X = {-b √ (b 2-4ac)}/(2a) to solve the quadratic equation, where a, b and c are quadratic, linear and constant coefficients respectively. However, it should be noted that this formula is only applicable if b 2-4ac > 0 is satisfied.