Answer:

Option D, 6 must be factored from 6x^2+18x

Step-by-step explanation:

Given : y=6x^2+18x+14

To find : The given equation in the form  y = a(x-h)^2+k  

Solution :

Now, we re-write the given equation

y=6x^2+18x+14

To covert it into vertex form y = a(x-h)^2+k where (h,k) represents the vertex.

First step is to take 6 common from 6x^2+18x

i.e, y=6(x^2+3x)+14      

Now, further step is by completing the square,

y=6(x^2+3x+frac{3}{2}^2-frac{3}{2}^2)+14  

y=6(x+frac{3}{2})^2-6times(frac{3}{2}^2)+14

y=6(x+frac{3}{2})^2-frac{27}{2}+14

y=6(x+frac{3}{2})^2+frac{1}{2}

The required form is y=6(x+frac{3}{2})^2+frac{1}{2}

Where, a=6, (h,k)=(-frac{3}{2},frac{1}{2})

Therefore, Option D is correct, 6 must be factored from 6x^2+18x