```
#' Deploy the quadratic formula given inputs \code{a}, \code{b}, and \code{c}
#' such that they satisfy the equation \code{(a * (x ^ 2)) + bx + c = 0}
#'
#' @param a The coefficient of the squared term
#' @param b The coefficient of the linear term
#' @param c The coefficient of the constant term
#'
#' @return The solutions to the equation
#'
#' @keywords internal
quadratic_formula <- function(a, b, c) {
if (a == 0) {
stop("The coefficient of the squared term must be greater than 0")
}
# The quadratic formula yields two solutions described by the formula:
# x = (-b +/- sqrt((b ^2) - (4 * a * c))) / (2 * a)
# First, find the solution using addition in the numerator
x_plus <- (-b + sqrt((b**2) - (4 * a * c))) / (2 * a)
# Then, repeat using subtraction
x_minus <- (-b - sqrt((b**2) - (4 * a * c))) / (2 * a)
# Combine the solutions into a single vector
solutions <- c(x_plus, x_minus)
# Return the solution
return(solutions)
}
#' Get the Euclidean distance between two points
#'
#' @param point_1_x A point's (or vector of points') \code{x} coordinate
#' @param point_1_y A point's (or vector of points') \code{y} coordinate
#' @param point_2_x A point's (or vector of points') \code{x} coordinate
#' @param point_2_y A point's (or vector of points') \code{y} coordinate
#'
#' @return The distance between the two supplied points
#'
#' @keywords internal
distance_formula <- function(point_1_x,
point_1_y,
point_2_x = 0,
point_2_y = 0) {
# Calculate the distance between the points
dist <- sqrt(
(
((point_2_x - point_1_x)^2) +
((point_2_y - point_1_y)^2)
)
)
# Return the distance calculated above
return(dist)
}
```

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