Maths

This is an inline $a^*=x-b^*$ equation.

These are block equations:

\[a^*=x-b^*\]\[ a^*=x-b^* \]\[ a^*=x-b^* \]

These are also block equations:

$$a^*=x-b^*$$$$ a^*=x-b^* $$$$ a^*=x-b^* $$

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

‍ ‍‍$y = (4x - 1)(x + 1)(x + 2) + 5)$