Quadratic functions and equations
A quadratic function is a type of function that can be described by the equation f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0. Quadratic functions produce a U-shaped curve called a parabola.
Quadratic equations are equations that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants. To solve a quadratic equation, you can use methods such as factoring, completing the square, or using the quadratic formula.
The graph of a quadratic function is a parabola that opens upwards if the coefficient of x^2 (a) is positive, and opens downwards if the coefficient of x^2 is negative.
Quadratic functions and equations are widely used in mathematics and science to model various real-world situations, such as projectile motion, the shape of bridges, and the behavior of certain physical systems.