Algebra 2 Calculator

Q: What is i in math, and what is i squared?

i is the imaginary unit. It stands for √−1, so i² = −1 . Powers of i repeat in a cycle of four: i = i, i² = −1, i³ = −i, i⁴ = 1. To find a big power, divide the exponent by 4 and use the remainder. For example, i²⁷ has remainder 3, so i²⁷ = −i.

Q: How do you rewrite a logarithm as an exponent?

A log asks "what power?" The rule is: log b (x) = y means b y = x So log₃(81) = 4 because 3⁴ = 81. The base stays the base, the answer becomes the exponent, and the number inside the log is the result.

Q: What is the compound interest formula?

A = P(1 + r/n) nt P = money you start with r = yearly rate as a decimal (4.5% = 0.045) n = times it compounds per year (12 for monthly, 4 for quarterly) t = years For interest compounded all the time, use A = Pe rt .

Algebra 2 Calculator

Updated Sep 9, 2026 By Jehan Wadia

Introduction

This Algebra 2 calculator solves the math you see in a high school Algebra 2 class. Type in your problem, and it shows the answer plus the steps to get there.

You can use it to:

Solve equations: linear, quadratic, cubic, and quartic
Graph functions and see zeros, holes, and asymptotes
Solve systems of 2 or 3 equations
Divide and factor polynomials
Work with complex numbers
Add, multiply, and invert matrices, and find determinants
Solve logs, exponents, compound interest, and half-life
Name conic sections like circles, ellipses, and hyperbolas
Find terms and sums of sequences, plus binomial expansions
Solve polynomial and rational inequalities
Find mean, median, standard deviation, z-scores, and probability

Pick a tab, fill in the boxes, and press Calculate. The keypad helps you type symbols like ^ and √. If you get stuck, click Example to load a sample problem. Click Reset to start over.

How to use our Algebra 2 Calculator

Start on the tab that matches your problem, type your numbers or equation, and press Calculate. You get the answer and the steps, so you can check your work on equations, graphs, systems, polynomials, complex numbers, matrices, logs, conics, sequences, inequalities, and stats.

Equations tab

Equation type: Choose linear, quadratic, or polynomial so the right boxes show up.

Coefficients (a₄, a₃, a₂, a₁, a₀): Type the number in front of each power of x. Use 0 if a term is missing.

Solve method: Pick factoring, the quadratic formula, or completing the square to see those steps.

Graphing tab

f(x): Type your first function, like (x^2 - 1)/(x - 2).

g(x): Type a second function if you want to compare two graphs.

X min and X max: Set the left and right edge of the graph window.

Evaluate at x: Type one x value to get the y value at that point.

a, h, and k sliders: Slide these to stretch, shift left or right, and shift up or down.

Systems tab

System size: Choose 2 equations with 2 variables or 3 with 3.

Coefficients and constants: Type the number for each variable in each row, then the number after the equals sign.

Method: Pick substitution, elimination, or matrix to see that way worked out.

Polynomials tab

Polynomial P(x): Type the full polynomial, like 2x^4 - 3x^3 - 15x^2 + 32x - 12.

Divisor Q(x): Type what you are dividing by for long division.

Value c: Type one number to test a root with synthetic division.

Complex numbers tab

First number (real and imaginary): Type the a part and the b part of a + bi.

Second number (real and imaginary): Type the a and b parts of the second complex number.

Power: Type a whole number to raise the first number to that power.

Angle units: Choose degrees or radians for the polar form answer.

Matrices tab

Operation: Pick add, multiply, inverse, determinant, or solve.

Rows and columns: Set the size of matrix A and matrix B to build the grids.

Matrix entries: Type a number in each box of the grids.

Exponentials and logs tab

Log base and argument: Type the base and the number inside the log, like base 3 and 81.

Exponential target: Type the value you want the exponential to equal.

Principal, rate, compounds per year, and time: Type your starting money, the yearly percent, how many times it compounds, and how long.

Starting amount, half-life, and elapsed time: Type how much you start with, the half-life, and how much time has passed. Pick the time units.

Conics tab

A, C, D, E, and F: Type the coefficients from Ax² + Cy² + Dx + Ey + F = 0 to name the conic and find its center, vertices, and foci.

Sequences tab

Sequence type: Choose arithmetic or geometric.

First term a₁: Type the starting term.

Common difference d: Type what you add each time in an arithmetic sequence.

Common ratio r: Type what you multiply by each time in a geometric sequence.

Term number n: Type which term you want to find.

How many terms: Type how many terms to list and add up.

Binomial a, b, and n: Type the two terms and the power for (a + b)ⁿ expansion.

Inequalities tab

Numerator: Type the top expression, like x^3 - 4x.

Denominator: Type the bottom expression, or 1 if there is none.

Sign: Choose <, >, ≤, or ≥.

Compare to k: Type the number on the other side, often 0.

Statistics tab

n and r: Type the total items and how many you choose for permutations and combinations.

Binomial n, k, and p: Type the number of trials, the number of successes, and the chance of success.

Data set: Type your numbers with commas between them to get mean, median, and standard deviation.

x, mean, and standard deviation: Type these three to get a z-score.

Extra buttons

Keypad: Tap the symbol buttons to add things like ^2, x, or parentheses to the box you last clicked.

Example: Loads a sample problem for the tab you are on.

Reset: Clears everything back to the starting values.

High contrast: Turn this on for darker, easier-to-read colors.

What Is Algebra 2?

Algebra 2 is the math class you take after Algebra 1 and Geometry. It builds on solving for x and adds new kinds of numbers, functions, and graphs. Most of the topics show up again in Precalculus, Calculus, and on tests like the SAT and ACT.

Main Algebra 2 Topics

Equations: Linear, quadratic, cubic, and higher degree equations. You can solve them by factoring, using the quadratic formula, or completing the square. Answers may be real or imaginary.
Functions and graphs: Every function has a domain (allowed x values) and a range (possible y values). Changing a, h, and k in a rule like a·f(x − h) + k stretches, flips, or slides the graph.
Systems of equations: Two or three equations that share the same answers. You can solve them by substitution, elimination, or with matrices.
Polynomials: Expressions like 2x⁴ − 3x³ + 5. You can divide them, find their roots (zeros), and factor them.
Complex numbers: Numbers with a real part and an imaginary part, written a + bi, where i² = −1. They let you solve equations that have no real answer.
Matrices: Boxes of numbers in rows and columns. You can add, multiply, find a determinant or inverse, and use them to solve systems fast.
Exponents and logarithms: Exponential growth doubles or shrinks things quickly. A logarithm undoes an exponent, so it answers "what power do I need?" These model interest, population, and half-life.
Conic sections: Circles, ellipses, parabolas, and hyperbolas. Each comes from a second degree equation in x and y.
Sequences and series: Arithmetic lists add the same number each time. Geometric lists multiply by the same number. A series is the sum of the terms.
Inequalities: Instead of one answer, you get a range of answers, often written as an interval like [−2, 3).
Statistics and probability: Mean, median, standard deviation, permutations, combinations, binomial probability, and z-scores.

Tips That Help

Always set the equation equal to zero before you factor.
A quadratic's discriminant (b² − 4ac) tells you the answer type: positive means two real roots, zero means one, negative means two complex roots.
You cannot divide by zero, so check the denominator when finding domain.
When you multiply or divide an inequality by a negative number, flip the sign.
Check your answer by plugging it back into the original problem.

Formulas used

Quadratic formula (equation solver)

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Linear system / matrix equation solution

A\mathbf{x} = \mathbf{b} \quad\Longrightarrow\quad \mathbf{x} = A^{-1}\mathbf{b}, \qquad x_i = \frac{\det(A_i)}{\det(A)}

De Moivre's theorem (complex power)

\left[r(\cos\theta + i\sin\theta)\right]^n = r^n\left(\cos n\theta + i\sin n\theta\right),\quad r = \sqrt{a^2+b^2},\ \theta = \operatorname{atan2}(b,a)

Logarithm by change of base

\log_b a = \frac{\ln a}{\ln b}

Compound interest

A = P\left(1 + \frac{r}{n}\right)^{nt}

Half-life exponential decay

N(t) = N_0\left(\frac{1}{2}\right)^{t/h}

Geometric sequence term and partial sum

a_n = a_1 r^{\,n-1}, \qquad S_n = a_1\,\frac{1 - r^n}{1 - r}\ (r \ne 1)

Binomial theorem expansion

(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{\,n-k} b^{\,k}, \qquad \binom{n}{k} = \frac{n!}{k!\,(n-k)!}

Frequently asked questions

What grade do you take Algebra 2 in?

Most students take Algebra 2 in 10th or 11th grade. It usually comes after Algebra 1 and Geometry. Some students who move fast take it in 9th grade instead.

Many colleges want to see Algebra 2 on a high school transcript, and its topics show up on the SAT and ACT.

What is the quadratic formula?

For any equation written as ax² + bx + c = 0, the answers are:

x = (−b ± √(b² − 4ac)) / (2a)

It works on every quadratic, even ones that will not factor. Set the equation equal to zero first, then plug in a, b, and c. The ± sign means you get two answers.

What is the rational root theorem?

It gives you a list of the fractions that could be roots of a polynomial. Take every factor of the last number (the constant) and divide it by every factor of the first number (the leading coefficient). Use plus and minus signs.

Example: for 2x³ + x² − 7x − 6, possible roots are ±1, ±2, ±3, ±6, ±1/2, ±3/2. Test them until one gives zero.

How does synthetic division work?

It is a fast way to divide a polynomial by x − c.

Write the coefficients in a row. Use 0 for missing terms.
Write c in the corner and bring the first coefficient down.
Multiply by c, add to the next coefficient, and repeat.

The last number is the remainder. If it is 0, then c is a root and x − c is a factor.

What is the difference between a hole and a vertical asymptote?

Both come from a zero in the denominator, but they act differently.

Hole: the factor cancels with the same factor on top. The graph has one missing point there.
Vertical asymptote: the factor stays only in the bottom. The graph shoots up or down and never touches that line.

Always factor the top and bottom before you decide.

What is i in math, and what is i squared?

i is the imaginary unit. It stands for √−1, so i² = −1.

Powers of i repeat in a cycle of four: i = i, i² = −1, i³ = −i, i⁴ = 1. To find a big power, divide the exponent by 4 and use the remainder. For example, i²⁷ has remainder 3, so i²⁷ = −i.

Why can't you multiply every pair of matrices?

The inside numbers must match. To multiply A × B, the number of columns in A must equal the number of rows in B.

A 2×3 times a 3×4 works, and the answer is 2×4. A 2×3 times a 2×3 does not work. Also, order matters: A × B usually does not equal B × A.

What does the determinant of a matrix tell you?

The determinant is one number that describes a square matrix.

If it is not zero, the matrix has an inverse and the system has exactly one solution.
If it is zero, there is no inverse. The system has no solution or infinitely many.

For a 2×2 matrix [a b; c d], the determinant is ad − bc.

How do you rewrite a logarithm as an exponent?

A log asks "what power?" The rule is:

log_b(x) = y means b^y = x

So log₃(81) = 4 because 3⁴ = 81. The base stays the base, the answer becomes the exponent, and the number inside the log is the result.

What is the compound interest formula?

A = P(1 + r/n)^nt

P = money you start with
r = yearly rate as a decimal (4.5% = 0.045)
n = times it compounds per year (12 for monthly, 4 for quarterly)
t = years

For interest compounded all the time, use A = Pe^rt.

What is the half-life formula?

N = N₀ · (1/2)^t/h

N₀ is the starting amount, t is the time that passed, and h is the half-life. Every time t equals one half-life, the amount drops by half.

Example: 250 g with a 12.3 year half-life, after 30 years, leaves 250 · (0.5)^30/12.3 ≈ 46 g.

How do you find the sum of an infinite geometric series?

Use S = a₁ / (1 − r), but only when |r| < 1.

a₁ is the first term and r is the number you multiply by each time. If |r| is 1 or bigger, the terms never shrink, so the sum grows forever and there is no answer.

Example: 8 + 4 + 2 + 1 + … has a₁ = 8 and r = 0.5, so the sum is 8 / 0.5 = 16.

How can you tell if an equation is a circle, ellipse, parabola, or hyperbola?

Look at the x² and y² terms in Ax² + Cy² + Dx + Ey + F = 0.

Circle: both squared, same number in front, same sign.
Ellipse: both squared, same sign, different numbers.
Hyperbola: both squared, opposite signs.
Parabola: only one variable is squared.

What is a z-score and what does it mean?

A z-score says how many standard deviations a value sits from the mean.

z = (x − μ) / σ

A positive z is above average, negative is below. A z of 2 means the value is 2 standard deviations above the mean, which is unusual. About 95% of normal data falls between z = −2 and z = 2.

What is the difference between a permutation and a combination?

Order is the key.

Permutation: order matters, like ranking 1st, 2nd, 3rd. nPr = n! / (n − r)!
Combination: order does not matter, like picking a team. nCr = n! / (r!(n − r)!)

There are always more permutations than combinations for the same n and r.

How do you write an answer in interval notation?

List the smallest number first, then the largest, with a comma between.

Use a bracket [ ] when the endpoint is included (≤ or ≥).
Use a parenthesis ( ) when it is not included (< or >).
Always use parentheses with ∞ and −∞.
Use ∪ to join separate pieces.

Example: x ≤ −2 or 0 < x < 5 becomes (−∞, −2] ∪ (0, 5).

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