Answer:
Table B
Vertex is (3,-5)
Step-by-step explanation:
We are given with an equation of a parabola 
Let is convert it into standard form of a parabola

adding and subtracting 9 in the right hand side of the =


the first three terms of the right hand side forms the expression of square of difference

Hence

adding 5 on both sides we get

Comparing it with the standard equation of a parabola

where
and 
The vertex of
will be (0,0)
and thus vertex of
will be (3,-5)
Hence the Table B is our right answer
The large community college has 76 professors and 212 lecturers
<u>Solution:</u>
Given that,
Total number of faculty = 228
Let, the number of professors be p, then the number of lecturers will be 228 – p
They have 5 professors for every 14 lecturers.
Then, ratio of professors to lecturers is 5 : 14
Expressing the ratio as fractions, we get,

Plug in the values of number of professors and lecturers


So, community has 76 professors, then, it will have 288 – 76 = 212 lecturers.