#### Quadratics
**Quadratics:** $x^2 + bx + c = (x+m)(x+n)$ where $mn=c$, $m+n=b$
-**Difference of squares:** $a^2 - b=^2 = (a - b)(a + b)$
+**Difference of squares:** $a^2 - b^2 = (a - b)(a + b)$
**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):** $ax^2+bx+c=a(x-{b\over2a})^2+c-{b^2\over4a}$
Parallel lines - $m_1 = m_2$
Perpendicular lines - $m_1 \times m_2 = -1$
+
+
+## Cubic graphs
+
+$$y=a(x-b)^3 + c$$
+
+- $m=0$ at *stationary point of inflection*
+- 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 $b, c, d$
+
+
+## Quartic graphs
+
+$$y=ax^4$$
+
+$$=a(x-b)(x-c)(x-d)(x-e)$$
+
+$$=ax^4+cd^2 (c \ge 0)$$
+
+$$=ax^2(x-b)(x-c)$$
+
+$$=a(x-b)^2(x-c)^2$$
+
+$$=a(x-b)(x-c)^3$$
+
+where
+- $x$-intercepts at $x=b,c,d,e$