Algebra 2 Regents Reference Table & Formulas

The official Algebra II Reference Sheet, plus key Algebra 2 formulas, concepts, and vocabulary to know for the exam.

The official Algebra II Reference Sheet

Provided with every Algebra II Regents booklet. Current edition: Next Generation (current).

What's inside the Algebra II Reference Sheet:

Algebra II loves identities. Mark the trig section before you start; you'll go back to it more than once.

Formulas to know for the Algebra 2 Regents
Name	Formula	What it's for
Quadratic formula	$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$	Solves $ax^2+bx+c=0$. A negative discriminant gives complex roots in Algebra II.
Sum & product of roots	$r_1+r_2=-\dfrac{b}{a},\quad r_1 r_2=\dfrac{c}{a}$	Read relationships between the roots straight off the coefficients.
Logarithm laws	$\log(ab)=\log a+\log b,\ \log\tfrac{a}{b}=\log a-\log b,\ \log a^n=n\log a$	Products become sums, quotients become differences, powers come down front.
Exponential / log inverse	$b^{y}=x \iff \log_b x = y$	Logs undo exponentials. Use this to get the variable out of an exponent.
Change of base	$\log_b x=\dfrac{\ln x}{\ln b}$	Lets you evaluate any base on a calculator.
Compound & continuous interest	$A=P\!\left(1+\tfrac{r}{n}\right)^{nt},\quad A=Pe^{rt}$	Discrete compounding n times a year, or continuous growth at rate r.
Arithmetic sequence & series	$a_n=a_1+(n-1)d,\quad S_n=\tfrac{n}{2}(a_1+a_n)$	Common difference d is added each step. The sum averages the first and last term.
Geometric sequence & series	$a_n=a_1 r^{\,n-1},\quad S_n=\dfrac{a_1(1-r^n)}{1-r}$	Common ratio r is multiplied each step.
Pythagorean identity	$\sin^2\theta+\cos^2\theta=1$	The most-used trig identity; rearrange to find a missing sine or cosine.
Radian measure	$\pi\text{ rad}=180^\circ$	Convert by multiplying by pi/180 (deg to rad) or 180/pi (rad to deg).

Imaginary & complex numbers — $i=\sqrt{-1}$, so $i^2=-1$. A complex number is $a+bi$; its conjugate $a-bi$ is used to rationalize and shows up in pairs of roots.
End behavior — Decided by the leading term. Even degree: both ends go the same way; odd degree: opposite ways. Positive lead coefficient lifts the right end.
Rational functions & asymptotes — Vertical asymptotes where the denominator is zero (and the numerator is not). Watch domain restrictions from denominators and even roots.
Inverse functions — Swap x and y and solve. The graph of an inverse is the reflection of the original across the line $y=x$.
Sinusoidal graphs — For $y=A\sin(Bx)+D$: amplitude is |A|, period is $2\pi/B$, and D is the midline (vertical shift).
Probability — Independent events multiply: $P(A\text{ and }B)=P(A)P(B)$. Conditional probability is $P(A\,|\,B)=P(A\text{ and }B)/P(B)$.

Discriminant — $b^2-4ac$. Negative means two complex roots; zero means a repeated real root.
Conjugate — $a-bi$ is the conjugate of $a+bi$. Complex roots of real polynomials always come in conjugate pairs.
Asymptote — A line a graph approaches but never reaches (vertical, horizontal, or slant).
Common difference / ratio — The fixed amount added (arithmetic) or multiplied (geometric) between consecutive terms.
Amplitude / period — Amplitude is half the height of a wave; period is the horizontal length of one full cycle.
Extraneous solution — A value that appears while solving (often radical or log equations) but fails in the original equation. Always check.

Do you get a reference table on the Algebra 2 Regents?

Yes. The official Algebra II Reference Sheet is provided with every Algebra 2 Regents booklet, so practice with it open.

What formulas do you need for the Algebra 2 Regents?

The most-used Algebra 2 formulas are on this page with what each one is for. There are 10 key formulas to know.