Algebra 1 Regents Reference Table & Formulas
The official Algebra I Reference Sheet, plus key Algebra 1 formulas, concepts, and vocabulary to know for the exam.
The official Algebra I Reference Sheet
Provided with every Algebra I Regents booklet. Current edition: Next Generation (current).
What's inside the Algebra I Reference Sheet:
- Conversion factors, customary and metric
- Area, surface area, and volume formulas for common shapes
- Pythagorean theorem and distance formula
- Quadratic formula
- Arithmetic and geometric sequence formulas
- Exponential growth / decay form
Use what's printed; don't burn brain on memorizing what's already there. Practice locating each table in <8 seconds so exam time goes to thinking, not flipping.
Key Algebra 1 formulas
| Name | Formula | What it's for |
|---|---|---|
| Slope | $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ | How fast y changes per unit of x. The defining quantity of a linear function. |
| Slope-intercept form | $y = mx + b$ | Line with slope m and y-intercept b. Read off m and b directly. |
| Point-slope form | $y - y_1 = m(x - x_1)$ | Write a line through any known point with any known slope. |
| Quadratic formula | $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ | Solves any quadratic $ax^2 + bx + c = 0$. Use when it won't factor cleanly. (Also on the official sheet.) |
| Discriminant | $D = b^2 - 4ac$ | D > 0: two real roots. D = 0: one repeated. D < 0: no real roots. |
| Vertex form | $y = a(x - h)^2 + k$ | Vertex sits at (h, k). Sign of a tells you if the parabola opens up or down. |
| Axis of symmetry | $x = -\dfrac{b}{2a}$ | The vertical line through the vertex of $y = ax^2 + bx + c$. |
| Distance formula | $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ | Pythagoras for two points in the plane. (On the official sheet.) |
| Midpoint formula | $M = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)$ | Average the x's and the y's. |
| Exponential growth | $y = a(1 + r)^t$ | Starts at a, grows by rate r each period t. Decay: replace + with −. (On the official sheet.) |
| Compound interest | $A = P\!\left(1 + \dfrac{r}{n}\right)^{nt}$ | Principal P at annual rate r compounded n times a year for t years. |
Key concepts
- Function vs relation — A function gives exactly one y for each x, graph passes the vertical-line test.
- Domain and range — Domain is the set of legal inputs (x). Range is the set of outputs (y). On the Regents, watch for square roots and denominators.
- Solutions of a system — Solving $\{Ax + By = C, Dx + Ey = F\}$ means finding (x, y) on both lines. Parallel lines: no solution. Same line: infinitely many.
- Zeros / roots / x-intercepts — All three names for the same thing: the x-values where y = 0.
- Linear vs nonlinear — Linear: constant rate of change. Quadratic: rate of change itself is linear. Exponential: multiplied (not added) over equal intervals.
- Vertex — The single highest or lowest point of a parabola. Maximum if a < 0, minimum if a > 0.
- Average rate of change — $\dfrac{f(b) - f(a)}{b - a}$, the slope of the line connecting the endpoints. Constant for linear functions only.
- Statistics: spread vs center — Center: mean / median. Spread: range / IQR / standard deviation. Skewed data → median over mean.
Must-know vocabulary
- Polynomial — A sum of terms like $3x^2 - 5x + 7$. Monomial (1 term), binomial (2), trinomial (3).
- Coefficient — The number multiplying the variable. In $-4x^2$, the coefficient is $-4$.
- Term — A single piece of an expression, separated by + or −. $5x - 3$ has two terms.
- Like terms — Same variable to the same power. $4x^2$ and $-x^2$ are like; $4x^2$ and $4x$ are not.
- Y-intercept — Where the graph crosses the y-axis, the value of y when x = 0.
- X-intercept — Where the graph crosses the x-axis. Same as a zero, root, or solution of f(x) = 0.
- Linear function — f(x) = mx + b. Straight line. Constant slope.
- Quadratic function — f(x) = $ax^2 + bx + c$ with a ≠ 0. Graph is a parabola.
- Exponential function — f(x) = $a \cdot b^x$ with b > 0, b ≠ 1. Multiplies, doesn't add.
- Inequality — Like an equation but with <, ≤, >, or ≥. Solution is a range, often shown on a number line.
- Interval notation — $(2, 5]$ means 2 < x ≤ 5. Parens exclude the endpoint; brackets include it.
Frequently asked questions
Do you get a reference table on the Algebra 1 Regents?
Yes. The official Algebra I Reference Sheet is provided with every Algebra 1 Regents booklet, so practice with it open.
What formulas do you need for the Algebra 1 Regents?
The most-used Algebra 1 formulas are on this page with what each one is for. There are 11 key formulas to know.