Η δικαιολογημένη απουσία φαίνεται στον έλεγχο προόδου.

Because δικαιολογημένη agrees with απουσία.

In Greek, adjectives and participles agree with the noun they describe in:

• gender
• number
• case

Here, απουσία is:

• feminine
• singular
• nominative

So the correct form is δικαιολογημένη.

A quick comparison:

• ο δικαιολογημένος μαθητής = the justified/excused male student
• η δικαιολογημένη απουσία = the justified/excused absence
• το δικαιολογημένο λάθος = the justified mistake

It is the passive participle of δικαιολογώ, used like an adjective.

So:

• δικαιολογώ = I justify / I excuse
• δικαιολογημένος, -η, -ο = justified, excused

In this sentence, it describes απουσία, so it works just like an adjective: excused absence or justified absence.

In school/administrative contexts, δικαιολογημένη απουσία usually means an absence that has been officially accepted as valid.

Η is the feminine singular definite article, meaning the.

It matches απουσία, which is feminine singular:

• η απουσία = the absence

Since the adjective is attached to the noun, the whole phrase becomes:

• η δικαιολογημένη απουσία = the excused absence

Greek articles also agree with the noun in gender, number, and case.

Because that is one of the normal Greek ways to place an adjective.

Greek commonly uses:

• article + adjective + noun
• article + noun + article + adjective

So:

• η δικαιολογημένη απουσία = the excused absence
• η απουσία η δικαιολογημένη = also possible, but more marked or formal

The first version is the natural one here.

So the structure is completely normal Greek:

• η = the
• δικαιολογημένη = excused
• απουσία = absence

Here φαίνεται means appears, is shown, or shows up.

The verb φαίνομαι can mean different things depending on context:

• seem
• appear
• be visible
• be shown

In this sentence, because it is followed by στον έλεγχο προόδου, the meaning is not it seems, but rather:

• it appears on the progress report
• it is shown on the progress report

So context tells you which English meaning fits.

Because φαίνομαι is a verb that normally appears in middle/passive form, but often has an active meaning.

So:

• φαίνομαι = I appear / I seem
• φαίνεται = it appears / it seems

This is very common in Greek. Not every middle/passive-looking form is truly passive in meaning.

Here:

• Η δικαιολογημένη απουσία φαίνεται... means
• The excused absence appears / is shown...

Στον is a contraction of:

• σε + τον = στον

It usually means in, on, at, or to, depending on context.

Here:

• στον έλεγχο = on the report / in the report

So στον is:

• the preposition σε
• plus the masculine singular article τον

This contraction is extremely common in modern Greek.

Because after σε, Greek normally uses the accusative case.

The dictionary form is:

• ο έλεγχος = the check / report

But after σε it becomes:

• στον έλεγχο

So:

• ο έλεγχος = nominative
• τον έλεγχο / στον έλεγχο = accusative

This is a very common pattern:

• ο μαθητής → στον μαθητή
• ο δρόμος → στον δρόμο
• ο έλεγχος → στον έλεγχο

This is a noun + genitive structure.

• έλεγχος = check, report, assessment
• πρόοδος = progress
• προόδου = of progress

So literally:

• έλεγχος προόδου = report/check of progress

In educational Greek, this phrase is commonly used for a progress report.

So the grammar is:

• στον έλεγχο προόδου = on the progress report

Because it depends on έλεγχος and shows a relationship like of progress.

Greek often uses the genitive where English might use:

• of
• a noun used as an adjective
• a compound noun

So:

• έλεγχος προόδου = report of progress = progress report

The noun πρόοδος changes to the genitive singular:

• η πρόοδος = progress
• της προόδου = of the progress
• in the phrase: έλεγχος προόδου

Because Greek often leaves out the article in this kind of noun + genitive phrase when the meaning is general or institutional.

So:

• έλεγχος προόδου is a set expression, like progress report

You could have an article there in other contexts, but here it sounds natural without one.

Compare:

• έλεγχος προόδου = progress report
• ο έλεγχος της προόδου = the monitoring/checking of the progress

The version in your sentence is the standard compact expression.

Yes. Greek word order is more flexible than English.

The neutral order here is:

• Η δικαιολογημένη απουσία φαίνεται στον έλεγχο προόδου.

But Greek could move things around for emphasis, for example:

• Στον έλεγχο προόδου φαίνεται η δικαιολογημένη απουσία.

That would still mean the same basic thing, but the emphasis would shift slightly toward where it appears.

So Greek word order is flexible, but the original sentence is the most straightforward and natural version.