[english] start writing on "innovative perspective" prompt

diff --git a/methods/polynomials.md b/methods/polynomials.md
index 847a91c711f30896bdb5844aaafd11d4d071633b..afd4eabe2e1baf8c2ba149569b2cfd2600251d4e 100644 (file)
--- a/methods/polynomials.md
+++ b/methods/polynomials.md
@@ -1,3 +1,7 @@
+---
+geometry: margin=1.5cm
+---
+
 # Polynomials
 
 ## Factorising
@@ -32,12 +36,12 @@ Distance: $\vec{AB} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
 
 ## Cubic graphs
 
-$$y=a(x-b)^3 + c$$
+$$y=a(bx-h)^3 + c$$
 
-- $m=0$ at *stationary point of inflection*
+- $m=0$ at *stationary point of inflection* (i.e. ({h \over b}, k)$)
 - in form $y=(x-a)^2(x-b)$, local max at $x=a$, local min at $x=b$
 - in form $y=a(x-b)(x-c)(x-d)$: $x$-intercepts at $b, c, d$
-
+- in form $y=a(x-b)^2(x-c)$, touches $x$-axis at $b$, intercept at $c$
 
 ## Quartic graphs
 
@@ -59,7 +63,7 @@ Equations with multiple pronumerals. Solutions are expressed in terms of pronume
 - **Infinitely many solutions** - lines are equal
 - **No solution** - lines are parallel
 
-### Solving $\begin{cases}px + qy = a \\ rx + sy = b\end{cases}$ for one, infinite and no solutions
+### Solving $\protect\begin{cases}px + qy = a \\ rx + sy = b\protect\end{cases}$ for one, infinite and no solutions
 
 where all coefficients are known except for one, and $a, b$ are known
 
@@ -79,12 +83,12 @@ where all coefficients are known except for one, and $a, b$ are known
 
 Or use Matrix -> `det` on CAS.
 
-### Solving $\begin{cases}a_1 x + b_1 y + c_1 z = d_1 \\
+### Solving $\protect\begin{cases}a_1 x + b_1 y + c_1 z = d_1 \\
 a_2 x + b_2 y + c_2 z = d_2 \\
-a_3 x + b_3 y + c_3 z = d_3\end{cases}$
+a_3 x + b_3 y + c_3 z = d_3\protect\end{cases}$
 
 - Use elimination
 - Generate two new equations with only two variables
 - Rearrange & solve
 - Substitute one variable into another equation to find another variable
-- etc.
\ No newline at end of file
+- etc.