Hey thanks for all your help but you kinda confused me on a few:

Question

1)Determine whether f(x)=-5x^2-10x+6 has a maximum or minimum value and find that value
A.minimum -1
B.maximum 11
C.maximum -1
D.minimum 11
and you said the function opens up, so there is a minimum.
it occurs when x=-1, and that minimum is f(-1), which is 11. So the answer is D right?

2)Identify the vertex,axis of symmetry,and direction of opening for y=1/2(x-8)^2+2
A.(8,2);x=-8;up
B.(-8,-2);x=-8;down
C.(8,-2);x=8;up
D.(8,2);x=8;up
I picked A,here is your reasoning.vertex is ok, but how can the axis of symmetry be x=-8?? Would it not go through the vertex?? So it is x=9 (always the same as the x of the vertex)

3)Which quadratic function has its vertex at(-2,7)and opens down?
A.y=-3(x+2)^2+7
B.y=(x-2)^2+7
C.y=-12(x+2)^2-7
D.y=-2(x-2)+7

4)Write y=x^2+4x-1 in vertex form.
A.y=(x-2)^2+5
B.y=(x+2)^2-5
C.y=(x+2)^2-1
D.y=(x+2)^2+3

Well I'm not Reiny but I can help you out with #3
I found out by plugging it into the Y=
for creating graphs on my TI-83 Plus that it is A.
You should be able to do the same if you have this calculator and plug in each function. Then hit graph

For #1 contrary to what you found I found that when I plugged it into my Y= function on my calculator that the
-curve faced down
-at X=-1 was the vertex
-Y=10.9/ 11

- based on that I would have to say my conclusion is that it has a maximum at Y=11

For #2 it is D
but not x=9 like you said but I assume it was a typo

The axis of symetry is the same as the x of the vertex (your thinking is correct)

1. yes it is D
2. I clearly meant to type x=8
3. clearly A. B would have vertex (2,7), and both C and D open downwards

4. y=x^2+4x-1
y = x^2 + 4x + 4 - 4 - 1
= (x+2)^2 - 5