Please help I’m completely lost and don’t have any clue what I’m doing

  D.  (-2, -7)

Step-by-step explanation:

I find the easiest way to locate the vertex or x-intercepts is to use a graphing calculator (see below). The vertex is the extreme point on the graph. For this function, it is (-2, -7), choice D.

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The axis of symmetry of the graph is the vertical line such that every point on the left is a mirror image of the corresponding point on the right. Here, that axis of symmetry is x=-2. (It is shown as a dashed orange line on the graph.)

The location of the axis of symmetry for quadratic ...

  y = ax^2 +bx +c

is x = -b/(2a).

For your function,

  y = 2x^2 +8x +1

the coefficients are a = 2, b = 8, c = 1. This means the axis of symmetry is ...

  x = -b/(2a) = -8/(2(2)) = -2

The vertical line at x=-2 is the axis of symmetry.

The vertex is on the axis of symmetry. Its y-value is found by evaluating the function for x = -2 (the x-value of the axis of symmetry).

  y = 2·(-2)^2 +8(-2) +1 = 2·4 -8·2 +1 = 8 -16 +1

  y = -7 . . . . at the vertex

So, the (x, y) coordinates of the vertex are (-2, -7).

D. (-2, -7)

Step-by-step explanation:

y= 2x²+8x+1

The vertex is max or min of the graph, for the given function it is

x = -b/2a for a>0

so x= - 8/4= -2

for the point of x= -2

y= 2*4 - 16 + 1 = - 7

So vertex is  (-2, -7), choice D.

the answer is c. 23/3