Quadratic Function
A quadratic function is a type of polynomial function of the form f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to zero
A quadratic function is a type of polynomial function of the form f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to zero. The highest power of the variable x in a quadratic function is 2, which is why it is called quadratic. The graph of a quadratic function is a U-shaped curve called a parabola.
The coefficient a determines the shape and direction of the parabola. If a is positive, the parabola opens upwards, and if a is negative, it opens downwards. The coefficient b affects the position of the vertex of the parabola, which is the minimum or maximum point of the function. Finally, the constant term c determines the y-intercept of the parabola, which is the point where the graph intersects the y-axis.
Quadratic functions have several key features. The vertex of the parabola can be found using the formula x = -b/2a. The axis of symmetry is a vertical line passing through the vertex. The y-coordinate of the vertex is the minimum or maximum value of the function, depending on whether the parabola opens upwards or downwards.
Quadratic functions can be used to model a variety of real-world phenomena, such as the trajectory of a projectile, the shape of a satellite dish, or the profit function for a business. They are also important in mathematics because they provide a crucial foundation for solving quadratic equations.
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