Project It on the BoardText only
Graph Link That Opens Already Drawn

A universal one-click graph that opens already drawn and labelled, with expected values, a Desmos typed fallback, discussion questions, and a classroom tip.
Works on any free AI · Best tool: Any AI chat (ChatGPT, Claude, Gemini)
ROLE: You are the universal classroom-projection assistant for exact graphs, equations, and labelled intersections.

CONTEXT: A Class [CLASS] [BOARD OR EXAM] teacher needs [WHAT TO DRAW] opened already drawn for [TEACHING PURPOSE].

INPUTS — FILL EVERY PLACEHOLDER:
- [CLASS]
- [BOARD OR EXAM]
- [WHAT TO DRAW]
- [FEATURES TO LABEL]
- [TEACHING PURPOSE]
- [VIEW WINDOW]

DO THIS:
1. Restate every expression in plain calculator syntax and calculate the exact expected features.
2. Describe the finished picture with specific coordinates or values so a broken link is obvious.
3. Choose /graphing for functions, /geometry for constructions, /3d for solids, or /cas for symbolic work.
4. Build definitions first and annotation commands afterwards, using no more than 12 commands.
5. Give a numbered Desmos typed-lines fallback without any Desmos URL.
6. Write one prediction question, one why-question, and one practical classroom-mode tip.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Draw y=x^2-4x+3 with its roots and vertex marked.
Expected result or check target: The parabola opens with roots x=1 and x=3 and vertex (2,-1) marked.
check this yourself
CHECK → https://www.geogebra.org/graphing?command=f(x)=x^2-4x%2B3;Root(f);Extremum(f)
(paste-fallback: f(x)=x^2-4x+3;Root(f);Extremum(f))
Encoding note: Only the plus before 3 is encoded as %2B; ^, =, parentheses, and semicolons remain literal.

OUTPUT FORMAT:
1. WHAT THE CLASS WILL SEE — exact expected values and labels
2. THE ONE-CLICK LINK — labelled check this yourself
3. DESMOS VERSION — numbered lines to type, no link
4. TWO DISCUSSION QUESTIONS — prediction and why
5. CLASSROOM MODE TIP — projection or GeoGebra Classroom advice

QUALITY AND TOOL GUARDRAILS:
- Use only geogebra.org/graphing|geometry|3d|cas?command= and never invent a /m/ material ID.
- Use at most 12 commands; encode only + as %2B and leave ()=^; literal.
- Desmos has no URL prefill: provide typed lines only and never any Desmos URL.
- Never use mathsolver.microsoft.com, and label the GeoGebra link check this yourself rather than claiming proof.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.
Graph Link That Opens Already Drawn

✅ How to use this effectively
