If the coefficient of the quadratic term is negative, the parabola opens downward. That eliminates choice A as an answer.
Set f(x)=0, and solve for x to find the zeros of the function (where the parabola crosses the x-axis)
That looks like choice B.
The x-coordinate of the vertex is in the general form
To find the y-coordinate of the vertex, find f(7/6) in your original function
You have to take the original function and complete the square in order to convert it to vertex form. Are you familiar with "completing the square"?
Step 1: Take half the coefficient of x and square it. That would be 1/2 of 10, which is 5 and 5 squared = 25. That's where I get the 25. I must add that value to the function in order to make a perfect square trinomial; namely
Step2: I can't forget about the 27 I already had, and I must subtract the 25 that I added to make my perfect square trinomial. Now everything is balanced again.
This is now in the form: where (h, k) is the vertex of the parabola.