5. Functions of the first and second degrees

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Mathematics is a crucial subject for the National High School Examination (ENEM) and one of the areas that most challenges students is First and Second Degree Functions. To gain a solid understanding of these concepts, it is important to study and practice extensively.

First Degree Functions

First-degree functions, also known as linear functions, are represented by the formula f(x) = ax + b, where "a" is the slope and "b" is the linear coefficient. The slope determines the slope of the line on the graph, while the linear coefficient indicates the point where the line crosses the y-axis.

To understand this better, let's consider the function f(x) = 2x + 3. Here, the slope is 2, which means that the line goes up two points for every point you move to the right. The linear coefficient is 3, which indicates that the line crosses the y-axis at point 3.

The main feature of the first degree function is that it will always form a straight line when plotted on a graph. Also, the first-degree function is always increasing or decreasing, depending on the sign of the slope.

Second Degree Functions

The quadratic functions, also known as quadratic functions, are represented by the formula f(x) = ax² + bx + c, where "a", "b" and "c" are constants and "a" is not equal to zero. The main feature of quadratic functions is that they form a parabola when plotted on a graph.

There are three main forms of a quadratic function: the canonical form, the factored form, and the polynomial form. Each of these shapes provides different information about the parable.

The canonical form is f(x) = a(x - h)² + k, where "h" and "k" are the coordinates of the vertex of the parabola. The factored form is f(x) = a(x - r)(x - s), where "r" and "s" are the roots of the equation. The polynomial form is the most common form, f(x) = ax² + bx + c.

To solve a quadratic function, we usually use the quadratic formula, which is x = [-b ± sqrt(b² - 4ac)] / (2a). This formula gives us the roots of the equation, which are the points where the parabola crosses the x-axis.

The quadratic functions have many practical applications, such as calculating trajectories of moving objects or optimizing the area of ​​a given space.

Conclusion

First and second degree functions are fundamental concepts in mathematics and are frequently tested in ENEM. Understanding these functions and how they are represented graphically is an important step in mastering ENEM math. Remember, constant practice is the key to success in math. So keep practicing problems and reviewing concepts to prepare for the exam.

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66. Exponential and logarithmic functions