"Where is the blue box?"
Translation:Wo ist der blaue Karton?
Why is this 'blaue' and not 'blau'? I thought that since it's Der Karton the adjective gets a masculine ending.
That is exactly why it goes "blaue" and not "blau". With the definite article, we have the weak inflexion, and the nominative ending for the masculine adjective is "-e", as shown here: https://en.wikipedia.org/wiki/German_adjectives#Weak_inflection
I don't think sein (English: be) is an intransitive verb. It is a linking verb and is often used with intransitive verbs.
Regardless, the "object" (predicate) of a linking verb remains Nominativ, thus "der Karton".
It'd be better to learn/use a German word for "box", such as der Kasten oder die Kiste oder der Behälter, than to use a borrowed English word.
How did people get Karton? When I said that, the answer changed to Kiste! Is my pronunciation that bad???
Did you get the gender wrong, perhaps?
der blaue Karton (masculine) but die blaue Kiste (feminine).
I entered der Karton and it said die Karton, then i entered die Karton and it said die Kiste.
die Karton is not correct.
I'm guessing that you misremembered what you saw, though I'm willing to be proved wrong by a screenshot so that we can try to figure out what might have gone wrong.
Why is there an umlaut on the "u" of blau in "Wo ist der blaü Karton"? (I was corrected when I omitted the umlaut)
As you may know, people who can't type ä ö ü ß can substitute ae oe ue ss instead -- Duo appears to consider those two sets of spellings as identical.
The correct spelling in this sentence is der blaue Karton, with root blau- and (weak, masculine nominative) ending -e.
blaü is nonsense in German; it's just a side-effect of how Duolingo treats umlaut replacements.