20 points! f(x)=x^2+6x+8 i need to find two seperate zeros which are a smaller x and a larger x, then the vertex of the parabola which is demonstrated by the equation. any is greatly appreciated, but give the answer with an explanation as well!

Basically, to solve this, we need to use the equation:
x^2 + 6x + 8 = 0
Now, to do this we need to simplify:
(x + 4)(x + 2) = 0
(When you multiply these two, you get x^2 + 6x + 8, you can check)
To make 0, one of these two have to make 0. In this case, one could be -4, and one could be -2
So, x = -4, and x = -2 (-2 is larger, -4 is smaller.)
Knowing this, we need to use -b/2a to find the vertex:
-6/2 = -3
Knowing that x is -3, we input it:
-9 + 18 - 8 = 1
Knowing this, we can say that the vertex is (-3, 1)

You can factor it by considering factors of 8 that add to 6.
  8 = 1·8 = 2·4
The latter pair add to 6, so your factorization is
  f(x) = (x + 2)(x + 4)
This product is zero when one of the factors is zero. There are 2 factors, hence 2 zeros of the function.
For x+2 = 0
  x = -2
For x+4 = 0
  x = -4

The graph of a parabola is symmetrical about its vertex, so the line of symmetry is halfway between the zeros, at x = (-2-4)/2 = -3. The y-coordinate of the vertex is the value of the function at this point,
  f(-3) = (-3+2)(-3+4) = -1

a) Your two separate zeros are
  x = -4 (smaller value)
  x = -2 (larger value)

b) The vertex of the parabola is
  vertex = (-3, -1)

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You can use a graphing calculator to answer these questions directly from the graph (or to check your work, as the case may be).