[methods] clarify cubic points of inflection

diff --git a/methods/polynomials.md b/methods/polynomials.md
index a2fe7b334ce874c55d9618fff171824c2a74f462..afd4eabe2e1baf8c2ba149569b2cfd2600251d4e 100644 (file)
--- a/methods/polynomials.md
+++ b/methods/polynomials.md
@@ -36,12 +36,12 @@ Distance: $\vec{AB} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
 
 ## Cubic graphs
 
 
 ## 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 $y=(x-a)^2(x-b)$, 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
 
 
 ## Quartic graphs
 


@@ -91,4 +91,4 @@ a_3 x + b_3 y + c_3 z = d_3\protect\end{cases}$
 - Generate two new equations with only two variables
 - Rearrange & solve
 - Substitute one variable into another equation to find another variable
 - 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.