Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already cover safety (readOnlyHint, idempotentHint, openWorldHint=false), so the bar is lower. The description nonetheless adds real behavioral context by disclosing what is returned (discriminant, real or complex roots, vertex) and that every step is written out. It omits edge behavior such as a=0 degenerating to a linear equation.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

Two compact sentences, front-loaded with the core operation and output list. The trailing web-page URL is mildly promotional but plausibly useful and not disruptive.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description carries the return-value burden and does so, naming discriminant, roots, and vertex. For a simple three-parameter calculator this is nearly complete; only edge cases like a=0 are unaddressed.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema coverage is 100%, with a, b, c documented and defaulted in the schema itself, so the baseline is 3. The description's equation form implies the mapping of a/b/c to their coefficients but adds no format, range, or validity detail beyond the schema.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

The description gives a specific verb ('Solve') and resource ('ax² + bx + c = 0 with the quadratic formula') and even enumerates the outputs (discriminant, real/complex roots, vertex). This is far more specific than the many generic siblings (scientific_calculator, square_root_calculator), though it never explicitly names an alternative to contrast against.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

Usage is only implied: an agent infers 'use when you have a quadratic equation.' There is no statement of when to use this versus scientific_calculator or any other math sibling, and no prerequisites or exclusions are given.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.