Polynomial Functions — Quick Reference Cheatsheet
A focused companion to the main Polynomial Functions topic page on SAT Math.
SAT Math Advanced Math One-page reference
This is a one-page reference for Polynomial Functions on the SAT math section. Use end behaviour, zeros and multiplicities to sketch the graph of a polynomial. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Polynomial Functions topic page.
What this topic is
A Polynomial Functions question tests fluency with non-linear relationships — quadratics, polynomials, exponentials, radicals, or rational expressions. These are the highest-leverage questions for moving from a 600 to a 700+.
Core formulas you must memorise
- Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a
- Discriminant: b² − 4ac
- Vertex form: y = a(x − h)² + k
- Difference of squares: a² − b² = (a − b)(a + b)
- Exponent rules: xᵃ · xᵇ = xᵃ⁺ᵇ ; (xᵃ)ᵇ = xᵃᵇ
If any of these formulas are not yet automatic, drill them via the Advanced Math formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.
How to spot this question type on the test
SAT questions on Polynomial Functions typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where Polynomial Functions is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.
The 30-second decision
Always factor first; reach for the quadratic formula only when factoring fails. After squaring or cross-multiplying, check candidates against the original equation for extraneous solutions.
If you have 60 seconds before the question
Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.
Drill set
Re-attempt the six worked Polynomial Functions questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.
Related study material
For broader test-prep tactics, see our Polynomial Functions strategy guide. For category-wide context, browse all Advanced Math topics. For score-targeted study plans, see the score-band guides.