Quadratic Function
A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0
A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. It is called quadratic because the highest power of the variable x is 2. The graph of a quadratic function is a curve called a parabola.
The coefficient a determines the shape of the parabola. If a > 0, the parabola opens upwards and has a minimum point. If a < 0, the parabola opens downwards and has a maximum point. The coefficient b affects the symmetry of the parabola, and the coefficient c determines the vertical shift of the parabola. The x-intercepts of a quadratic function can be found by setting f(x) = 0 and solving the resulting quadratic equation. These correspond to the points where the graph of the function intersects the x-axis. The y-intercept of a quadratic function can be found by evaluating f(0), which gives the value of the function at x = 0. Quadratic functions are commonly used to model real-life situations, such as the path of a projectile, the shape of a satellite dish, or the profit function in economics. They are also integral in solving various mathematical problems and are extensively studied in algebra and calculus.
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