The answer is B or it should be
The answer is b or the second choice available
dy%2Fdx+=+6x%5E2 So the slope at x = 2 is 6*(2^2) = 24
F(x)=x-5
When you plug in 0 for x, y = -5 as we want it to, so it checks out :)
Hope this helps!
As we know vertex -

Passes through (1,4). Substitute x = 1 and y = 4

Therefore the vertex equation is 
Since you want the "standard" form then..

So the standard form is 1/2x^2 + 3x + 1/2