Final answer:
A quadratic function is represented by y = ax²+bx+c and graphically produces a parabola. Solutions to quadratic equations can be found using the quadratic formula, yielding the roots of the function. Quadratic functions have diverse applications in science and engineering.
Step-by-step explanation:
A quadratic function is a mathematical function that can be written in the standard form y = ax²+bx+c, where a, b, and c are constants, and a is not equal to zero. This type of function is also referred to as a second-order polynomial. The curve produced by this function when graphed is known as a parabola, and it opens upwards if a is positive and downwards if a is negative.
When trying to find the solution of quadratic equations that are in the form ax²+bx+c = 0, you can use the quadratic formula where the solution or roots are given by x = (-b ± √(b²-4ac)) / (2a). This formula provides the exact values of x where the function crosses the x-axis, which are also known as the roots or zeroes of the function.
Especially in applications with physical data, quadratic equations often yield real roots, and commonly only the positive roots are of interest, depending on the context. Quadratic equations have significant applications in various fields such as physics, engineering, economics, and more.