Key Equations

general form of a quadratic function	$f (x) = a x^{2} + b x + c f (x) = a x^{2} + b x + c$
the quadratic formula	$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
standard form of a quadratic function	$f (x) = a {(x - h)}^{2} + k f (x) = a {(x - h)}^{2} + k$

general form of a polynomial function

f (x) = a_{n} x^{n} + a_{n - 1} x^{n - 1} + ... + a_{2} x^{2} + a_{1} x + a_{1} f (x) = a_{n} x^{n} + a_{n - 1} x^{n - 1} + ... + a_{2} x^{2} + a_{1} x + a_{1}

Division Algorithm

f (x) = d (x) q (x) + r (x) f (x) = d (x) q (x) + r (x)

where

q (x) \neq 0 q (x) \neq 0

Rational Function

f (x) = \frac{P (x)}{Q (x)} = \frac{a_{p} x^{p} + a_{p - 1} x^{p - 1} + ... + a_{1} x + a_{0}}{b_{q} x^{q} + b_{q - 1} x^{q - 1} + ... + b_{1} x + b_{0}}, Q (x) \neq 0 f (x) = \frac{P (x)}{Q (x)} = \frac{a_{p} x^{p} + a_{p - 1} x^{p - 1} + ... + a_{1} x + a_{0}}{b_{q} x^{q} + b_{q - 1} x^{q - 1} + ... + b_{1} x + b_{0}},

Direct variation	$y = k x^{n}, k is a nonzero constant . y = k x^{n}, k is a nonzero constant .$
Inverse variation	$y = \frac{k}{x^{n}}, k is a nonzero constant . y = \frac{k}{x^{n}}, k is a nonzero constant .$