Poop Sheet

Polynomials

https://www.khanacademy.org/test-prep/v2-sat-math/x0fcc98a58ba3bea7:advanced-math-easier/x0fcc98a58ba3bea7:polynomial-and-other-nonlinear-graphs-easier/e/v2-polynomial-and-other-nonlinear-graphs-1

\(f(x)=3x^3 - 7x^2 + 9x - 4\)

poly1 <- function(x) {
  y = 3 * x^3 - 7 * x^2 + 9 * x - 4
  return(y) 
}
svg("poly1.svg", width = 11, pointsize = 12, family = "sans")
curve(poly1, from = -3, to = 3, n = 40)
abline(h = 0)
abline(v = 0)
abline(h = -4, col = "red")
dev.off()

Polynomial graph

\(f(x)=2x^3 - 2x^2 + 18x - 18\)

poly2 <- function(x) {
  y = 2 * x^3 - 2 * x^2 + 18 * x - 18
  return(y) 
}
svg("poly2.svg", width = 11, pointsize = 12, family = "sans")
curve(poly2, from = -3, to = 3, n = 40)
abline(h = 0)
abline(v = 0)
abline(v = 1, col = "red")
dev.off()

Second poly

‍ ‍‍\(y = (4x - 1)(x + 1)(x + 2) + 5)\)

poly3 <- function(x) {
  y = (4*x - 1)*(x + 1)*(x + 2) + 5
  return(y) 
}
svg("poly3.svg", width = 11, pointsize = 12, family = "sans")
curve(poly3, from = -3, to = 3, n = 40)
abline(h = 0)
abline(v = 0)
abline(v = -1, col = "red")
dev.off()

Third poly

\(f(x)=x^4 + 4x^3 - 7x^2 - 22x + 24\)

poly4 <- function(x) {
  y = x^4 + 4 * x^3 - 7 * x^2 - 22 * x + 24
  return(y) 
}
svg("poly4.svg", width = 11, pointsize = 12, family = "sans")
curve(poly4, from = -4, to = 4, n = 40)
abline(h = 0)
abline(v = 0)
abline(v = -3, col = "red")
dev.off()

Fourth poly

\(r(q)=-0.31*(q - 260)^2 + 9500\)

poly5 <- function(q) {
  y = -0.31*(q - 260)^2 + 9500
  return(y) 
}
svg("poly5.svg", width = 11, pointsize = 12, family = "sans")
curve(poly5, from = 0, to = 500, n = 500)
abline(h = 0)
abline(v = 0)
abline(h = 9500, col = "red")
dev.off()

Fifth poly

poly6 <- function(t) {
  y = 24.5 - 4.9*t^2
  return(y) 
}
svg("poly6.svg", width = 11, pointsize = 12, family = "sans")
curve(poly6, from = 0, to = 2.5, n = 100)
abline(h = 0)
abline(v = 0)
abline(v = 2, col = "red")
abline(h = 4.9, col = "red")
dev.off()

Sixth poly