Quadratic Function
A quadratic function is a type of mathematical function that can be represented by an equation of the form f(x) = ax^2 + bx + c, where a, b, and c are constants
A quadratic function is a type of mathematical function that can be represented by an equation of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. The variable x represents the input to the function, and f(x) represents the output value.
The term “quadratic” comes from the Latin word “quadratus” meaning square, and this is because the highest power of x in the equation is squared (x^2).
The graph of a quadratic function is a symmetric curve called a parabola. The general shape of the parabola depends on the value of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. The constant term c determines the vertical shift of the parabola, while the coefficient b affects the symmetry and horizontal shift. The coefficient a is related to the steepness of the parabola. Quadratic functions are often used to model various real-world phenomena, such as projectile motion, the shape of a satellite dish, or the profit function of a business. To graph a quadratic function, you can determine the vertex of the parabola using the formula x = -b/(2a) and then find a few additional points to sketch the curve. Another approach is to find the x-intercepts (where the graph intersects the x-axis) by factoring the quadratic equation or using the quadratic formula. Quadratic functions also have several key properties, such as their domain (the set of all possible x-values), range (the set of all possible y-values), and the axis of symmetry (the vertical line that divides the parabola in half). In summary, a quadratic function is a mathematical function that can be represented by an equation of the form f(x) = ax^2 + bx + c. It produces a graph known as a parabola, which has various properties and can be used to model real-world phenomena.
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