Final answer:
A quadratic function is typically expressed as ax²+bx+c = 0, and its solutions are calculated using the quadratic formula. This equation is essential in many fields that require finding the maximum, minimum, or roots of functions.
Step-by-step explanation:
Quadratic functions, also known as second-order polynomials, are an integral part of mathematics, particularly in algebra. The general form of a quadratic equation is ax²+bx+c = 0, where a, b, and c are constants, and a is not equal to zero. The solutions to a quadratic equation are found using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a).
For example, if we have an equation like x²+ 1.2 x 10^-2x - 6.0 × 10^-3 = 0, we can identify a, b, and c and plug them into the quadratic formula to find the roots of the equation. These solutions are critical for various applications in physics, engineering, and finance, among other fields.