Which of the following is the minium value of the function a. -6b. 3/4c. -4d. 6

Begin by setting the equation = to 0, and then move the 6 over by subtraction.  Here's what it is now: .  Now we are ready to complete the square on the x terms.  First, though, the rule is that the leading coefficient has to be a +1.  Ours is a 3/4.  So we will factor it out.  When we do that, we get .  Take half the linear term, square it and add it to both sides.  Our linear term is 8.  Half of 8 is 4, and 4 squared is 16.  So add 16 to the left inside the parethesis...BUT don't forget about that 3/4 out front there, refusing to be ignored.  It is a multiplier. So what we have really added in is (3/4)(16), which is 12.  Now here's what we have: .  Simplifying the right side we have .  The whole point of this is to create a perfect square binomial on the left which will serve as the h in our vertex (the x-coordinate).  That binomial is this: .  Now we will move the 6 back over by subtraction and set it back equal to y.  .  The minimum value is reflected in the k value of the vertex (the y-coordinate), which is -6.  So our answer is A from above.