Master Algebra 2 from first principles
Functions, polynomials, exponentials, logarithms, and conic sections. Aligned to the Massachusetts Curriculum Frameworks for Algebra II.
Algebra 2 — Essential Formulas
Quadratic formula, logarithms, complex numbers, function transformations, sequences — every Algebra 2 essential on one page.
Function Transformations: Shift, Reflect, Stretch — One Equation Tells You Everything
Once you know the parent function, you can sketch any transformation by reading the equation. Master the four moves — vertical/horizontal shift, reflection, stretch — and you'll graph every quadratic, root, and absolute-value function on sight.
Inverse Functions: How to Reverse a Rule
An inverse function undoes the original. Swap x and y, solve for y — that's the whole technique. Plus the geometric meaning (reflection across y = x) and the horizontal-line test for invertibility.
Quadratic Functions Mastery: Vertex Form, Completing the Square, and the Discriminant
Algebra 1 introduced parabolas. Algebra 2 makes you fluent — switch between forms, complete the square in your head, and read the discriminant to know exactly how many real roots before solving.
Complex Numbers: When the Quadratic Formula Hits a Negative Discriminant
The imaginary unit i = √(−1) extends the number line into a plane. Master arithmetic with complex numbers, the conjugate trick for division, and you will handle every "no real solution" quadratic on the Regents.
Square Root, Cube Root, Cubic & Absolute Value Functions
Four parent functions, four shapes, four sets of rules. Domain restrictions for square roots, the symmetry of cube roots, the V of absolute value, and how transformations apply uniformly to all of them.
Exponential Functions Advanced: Continuous Growth, e, and Half-Life
Algebra 1 introduced exponential growth. Algebra 2 deepens it: the natural base e, continuous compounding, and decay problems where the half-life is measured in years.
Logarithmic Functions: The Inverse of Exponential
A logarithm asks "what exponent?" Master the definition, the three properties (product/quotient/power), and you will solve exponential equations of any base.
Rational Functions: Asymptotes, Holes, and the Forbidden Inputs
A rational function is a fraction of polynomials. Master vertical/horizontal asymptotes, where they come from, and the difference between an asymptote and a hole.
Polynomial Functions: End Behavior, Roots, and the Rational Root Theorem
The Fundamental Theorem of Algebra guarantees a polynomial of degree n has n roots. Master the Rational Root Theorem, end-behavior rules, and you'll factor polynomials too big for plain trial and error.
Sequences, Series & Conic Sections
Algebra 1 introduced arithmetic and geometric sequences. Algebra 2 sums them with closed-form formulas, and adds the four conic sections — circle, ellipse, parabola, hyperbola — recognized at sight from the equation.