Learn Hardcore Turkish: Öğrencinin potansiyeli yüksek.

Turkish vowel harmony makes the suffix vowel match the last vowel of the stem. Öğrenci ends in the front unrounded vowel e, so the genitive uses i. Because the stem ends in a vowel, a buffer consonant n is inserted, yielding -nin.

Why does potansiyel take the suffix -i in potansiyeli?

When a noun is possessed, the possessed noun must carry a 3rd-person singular possessive suffix.
• potansiyel + -i → potansiyeli = “his/her/its potential.”

Is the -i on potansiyeli the accusative case?

No. Although the 3rd-sg. accusative suffix is also -i, here it’s the possessive suffix. You can tell because the possessor (Öğrencinin) is in the genitive case.

Why isn’t there a verb “to be” (is) in this sentence?

Turkish uses a zero copula in the simple present: you state Subject + Predicate directly.
If you want a more formal or emphatic style, you can add -dir to the adjective:
• Öğrencinin potansiyeli yüksektir.

Why does the adjective yüksek come after the noun rather than before it like in English (“high potential”)?

Here yüksek is a predicate adjective, so it follows the subject noun phrase.
If you want an attributive adjective (“high potential”) you say yüksek potansiyel, but then you need a different structure to mean “has”:
• Öğrencinin yüksek potansiyeli var.

How would you say “A student’s potential is high” (indefinite “a student”)?

Add bir to the possessor for indefiniteness:
• Bir öğrencinin potansiyeli yüksek.

How do you express “The student has high potential” instead of “The student’s potential is high”?

Use the verb var (“there is/has”) with an attributive adjective before the noun:
• Öğrencinin yüksek potansiyeli var.

Can you drop the genitive and possessive suffixes and say Öğrenci potansiyeli yüksek?

No. Turkish grammar requires Öğrenci-nin (genitive) and potansiyel-i (3rd-sg. possessive) to mark “the student’s potential” clearly.