Quadratic function
A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constant coefficients, and x is the input variable
A quadratic function is a mathematical function of the form f(x) = ax^2 + bx + c, where a, b, and c are constant coefficients, and x is the input variable. The highest power of x in a quadratic function is 2, hence the term “quadratic,” which comes from the Latin word “quadratus” meaning “square.”
Graphically, a quadratic function forms a parabola, which is a U-shaped curve. The shape of the parabola and the behavior of the function depend on the values of the coefficients a, b, and c.
The coefficient a determines the direction of the parabola’s opening. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward.
The coefficient b affects the position of the parabola along the x-axis. If b is positive, the parabola shifts to the left, and if b is negative, the parabola shifts to the right.
The constant term c determines the y-intercept of the parabola, which is the point where the parabola intersects the y-axis.
Quadratic functions are widely used in various disciplines, such as physics, engineering, economics, and computer science, to model relationships characterized by quadratic behavior, such as projectile motion, profit and cost analysis, and optimization problems. They provide a useful mathematical tool for analyzing and solving real-world problems.
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