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quartic

Quartic - A quartic function (or bi-quadratic) is a polynomial of degree 4:

where . Solving general quartic equations analytically is more complex than quadratics but is still possible via Ferrari’s method or by decomposition.

R demonstration (plotting a quartic):

library(data.table)
library(ggplot2)
 
f_quartic <- function(x) x^4 - 2*x^3 + 3*x + 1
x_vals <- seq(-3,3, by=0.1)
dt_qr <- data.table(
  x = x_vals,
  y = f_quartic(x_vals)
)
 
ggplot(dt_qr, aes(x=x, y=y)) +
  geom_line(color="blue") +
  labs(
    title="Example Quartic: x^4 - 2x^3 + 3x + 1",
    x="x", 
    y="f(x)"
  ) +
  theme_minimal()

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