The difference between Peak and Vertex

When used as nouns, peak means a point, whereas vertex means the highest point of something.

Peak is also verb with the meaning: to reach a highest degree or maximum.

Peak is also adjective with the meaning: bad.

check bellow for the other definitions of Peak and Vertex

Peak as a noun:

A point; the sharp end or top of anything that terminates in a point; as, the peak, or front, of a cap.
Peak as a noun:

The highest value reached by some quantity in a time period.

Examples:

"synonyms: apex pinnacle Thesaurus:apex"

"The stock market reached a peak in September 1929."
Peak as a noun (geography):

The top, or one of the tops, of a hill, mountain, or range, ending in a point.

Examples:

"synonyms: summit top"

"They reached the peak after 8 hours of climbing."
Peak as a noun (geography):

The whole hill or mountain, especially when isolated.
Peak as a noun (nautical):

The upper aftermost corner of a fore-and-aft sail.

Examples:

"'peak-halyards"

"'peak-brails"
Peak as a noun (nautical):

The narrow part of a vessel's bow, or the hold within it.
Peak as a noun (nautical):

The extremity of an anchor fluke; the bill.
Peak as a noun (mathematics):

A local maximum of a function, e.g. for sine waves, each point at which the value of y is at its maximum.

Peak as a verb:

To reach a highest degree or maximum.

Examples:

"Historians argue about when the Roman Empire began to peak and ultimately decay."
Peak as a verb:

To rise or extend into a peak or point; to form, or appear as, a peak.
Peak as a verb (nautical, transitive):

To raise the point of (a gaff) closer to perpendicular.

Peak as a verb (intransitive):

To become sick or wan.
Peak as a verb (intransitive):

To acquire sharpness of figure or features; hence, to look thin or sickly.
Peak as a verb (intransitive):

To pry; to peep slyly.

Examples:

"rfquotek Shakespeare"

Vertex as a noun:

The highest point of something.
Vertex as a noun (anatomy):

The highest surface on the skull.
Vertex as a noun (geometry):

The common point of the two rays of the angle, or its equivalent structure in polyhedra (meeting of edges) and higher order polytopes.
Vertex as a noun (mathematics):

A point on the curve with a local minimum or maximum of curvature.
Vertex as a noun (graph theory):

One of the elements of a graph joined or not by edges to other vertices.
Vertex as a noun (computer graphics):

A point in 3D space, usually given in terms of its Cartesian coordinates.
Vertex as a noun (optics):

The point where the surface of a lens crosses the optical axis.
Vertex as a noun (nuclear, or, particle physics):

An interaction point.
Vertex as a noun (astrology):

The point where the prime vertical meets the ecliptic in the western hemisphere of a natal chart.