Final answer:
A user-defined function in math is written to calculate an output based on input variables. An example function, given the quadratic form, is f(x) = ax² + bx + c, which can be implemented in code to compute x,y data pairs for plotting.
Step-by-step explanation:
A user-defined function in mathematics typically involves creating an equation or set of instructions to calculate a value based on input variables. From the context of the question, it seems that the variables in question are coefficients and a variable xi. Although the question's coefficients are not clearly defined due to typographical errors, I will provide an example of a function based on a generic quadratic form, as suggested by the place-holder '-kx²' in the reference information.
Example User-Defined Function
Let's define a user-defined function f(x) = ax² + bx + c. Here, a, b, and c are coefficients, and x is an independent variable.
def user_defined_function(x, a, b, c):
return a * x ** 2 + b * x + c
To calculate y for a given xi (where xi denotes a specific value of x), you would call user_defined_function(xi, a, b, c) with your specific coefficients and value for xi.
Once this function has been defined, you can use it to compute x,y data pairs which can be plotted to visualize the relationship between x and y.