hoffnungsvoll
hopeful
Describes a person who looks to the future full of hope and confidence.
Trotz der Niederlage blieb der Trainer hoffnungsvoll für das nächste Spiel.
Despite the defeat, the coach remained hopeful about the next game.

hopeful
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hopeful
Describes a person who looks to the future full of hope and confidence.
Trotz der Niederlage blieb der Trainer hoffnungsvoll für das nächste Spiel.
Despite the defeat, the coach remained hopeful about the next game.

The adjective is made up of the noun 'die Hoffnung' (hope), the linking -s, and the word 'voll' (full). So it literally means “full of hope.”
Sie war hoffnungsvoll, dass alles gut werden würde.
She was hopeful that everything would turn out well.
'Hoffnungsvoll' (hopeful) can be used as an adjective before a noun, as part of the predicate with 'sein' (to be), or as an adverb to describe a verb.
Er warf ihr einen hoffnungsvollen Blick zu.
He gave her a hopeful look.
The word describes either a person's feeling or the potential of something. When it refers to a person, it means 'zuversichtlich' (confident/hopeful). When it describes a thing, such as a result or a talent, it means 'vielversprechend' (promising).
Der junge Pianist gilt als sehr hoffnungsvolles Talent.
The young pianist is considered a very promising talent.
hopefully
'hoffentlich' and 'hoffnungsvoll' look similar and both have to do with hope, but they are used differently. 'hoffentlich' is an adverb and expresses a wish for an event: you hope that something will happen. 'hoffnungsvoll' is an adjective. It describes a person who has hope, or a situation that gives reason for hope. That is why you do not say 'Ich bin hoffentlich' to describe the person, but 'Ich bin hoffnungsvoll'. 'hoffentlich' belongs more to the whole sentence.

Nach der guten Nachricht blickt die Familie hoffnungsvoll in die Zukunft.
After the good news, the family looks to the future with hope.
Hoffentlich hat er beim Training nichts vergessen.
Hopefully he didn't forget anything during training.