A brief of mathematics
Quadratic equations, also called quadratic equations, graphically represent a curved line, in the form of a parabola. The development of the problems allows us to find an observation of the graph for the algebraic resolution can be related by means of a simple calculation of derivatives, by means of a sequential procedure, even explaining the determination of the well-known general formula for solving quadratic equations.
Explanation:
Using the theorem of the derivative of a polynomial function, it allows us to find the increase or decrease of the function in question, when it tends to zero. It can be used, and align that trend to when the y or x axis goes to zero. In other words, it allows us to find the vertex of the quadratic function (parabola).
The subject of the derivative is made in relation to the instantaneous time to do it to its minimum infinitesimal expression.
The procedure:
- Let an equation be: ax^2 + bx + c, we transform to a function of the quadratic type, that is: f(x) = ax^2 + bx + c. And when d(x)= 1.
- Differentiate the function polynomially; f´(x) * d(f(x)) / dt = 2ax + b.
- Equate the derivative to zero (Implies the tendency to the intersection of axes); 2ax + b = 0.
- Solve for the value of x; -> x = (-b) / (2a).
- When we obtain and substitute the general formula for a quadratic equation.
- The found solution "x" is replaced in the main primitive function f(x), obtaining a value for "y"
- Both points indicate the coordinate of the vertex of the quadratic function, and in turn, the solution of the quadratic equation initially proposed
- In conclusion, the vertex is equivalent to the solution of a quadratic equation.
Finally, a direct relationship can be verified between the general formula and the vertex of the quadratic function found initially.
Will it work the same way in a cubic equation? And in a quadratic equation?
Sure, this type of analysis will serve to find the solutions of polynomial equations, however, the complexity and development increases as the degree of the equation increases or increases.
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