From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 4 Dec 2018 02:59:08 +0000 (+1100)
Subject: linear ez shit
X-Git-Tag: yr12~288^2~4
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/408a7b49a043970cc9ce7289900412a701bfaa3c?hp=ab4d2b7036f51b07e578e779d4bec5af2e61b8a0

linear ez shit
---

diff --git a/methods/polynomials.md b/methods/polynomials.md
index 6fadf11..e81e0b0 100644
--- a/methods/polynomials.md
+++ b/methods/polynomials.md
@@ -8,9 +8,16 @@
 **Perfect squares:** $a^2 \pm 2ab + b^2 = (a \pm b^2)$  
 **Completing the square (monic):** $x^2+bx+c=(x+{b\over2})^2+c-{b^2\over4}$  
 **Completing the square (non-monic):** $ax^2+bx+c=a(x-{b\over2a})^2+c-{b^2\over4a}$  
-**Quadratic formula:** $x={{-b\pm\sqrt{b^2-4ac}}\over2a}$ where $\Delta=b^2-4ac$
+**Quadratic formula:** $x={{-b\pm\sqrt{b^2-4ac}}\over2a}$ where $\Delta=b^2-4ac$ (if $\Delta$ is a perfect square, rational roots)
 
 #### Cubics
 **Difference of cubes:** $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$  
 **Sum of cubes:** $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$  
 **Perfect cubes:** $a^3 \pm 3a^2b + 3ab^2 \pm b^3 = (a \pm b)^3$  
+
+## Linear and quadratic graphs
+
+$$y=mx+c, \quad {x \over a} + {y \over b}=1$$
+
+Parallel lines - $m_1 = m_2$  
+Perpendicular lines - $m_1 \times m_2 = -1$