Can you help me with the vertex form, and the number of terms? (Algebra 2)

Rewrite the equation in vertex form.

y = 3/5x^2 + 30x + 382

is it

A: y = 3/5 (x +25)^2 + 7
B: y = (x + 30)^2 + 518
C: y = (3x/5 + 25)^2 + 7
D: y = 3/5 (c+5)^2 + 21/5

I picked A. Am I right?
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Classify -7x^5 - 6x^4 + 4x^3 by degree and by number of terms

A: quartic trinomial
B: Quintic trinomial
C: cubic binomial
D:quadratic binomial

I picked B.
Am I right?

The "vertex form" is just what you get by completing the square, so do that:

y = (3/5)x² + 30x + 382
= (3/5)(x² + 50x + 1910/3) ... factor out the leading term
= (3/5)[(x² + 50x + 625) + 1910/3 - 625] ... add and subtract 25² = 625
= (3/5)[(x + 25)² + 35/3] ... simplify inside [] brackets
= (3/5)(x + 25) + 7

So, you're right. I hope this is something like the reason you picked A... :^)

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Yes, you got both right.