Which statement is true concerning the vertex and axis of symmetry of h(x)=−2x2+8x?
the vertex is at (0, 0) and the axis of symmetry is x = 2.
the vertex is at (0, 0) and the axis of symmetry is y= 2.
the vertex is at (2, 8) and the axis of symmetry is x = 2. '
the vertex is at (2, 2) and the axis of symmetry is y = 2.

c)

One way I did the problem: I provided work through elimination of choices (without any computations).

Second way I did the problem: I went through all the steps to actually find the vertex and the axis of symmetry.

Step-by-step explanation:

The vertex is given by:

.

The axis of symmetry of a parabola function is always going to be a vertical line and is in the case of the vertex being it would be .

So we can already rule out the following choices without any computations:

a can be ruled out since 0 is not 2.

b can be rules out because that is y=2 and not x=2. Even if it was x=2, it doesn't match the 0 x-coordinate in the vertex.

c is a possibility

d can be ruled out because that is y=2 and not x=2.

---

c is the only possibility so it has to be the answer but let's confirm.

Plug into the x-coordinate of the vertex:

So the axis of asymmetry is x=2 and the x-coordinate of the vertex is 2.

To find the corresponding y-coordinate we just plug 2 into our function:

.

So the vertex is (2,8) and the axis of symmetry is x=2.

Big note: If we weren't given that it was a function; like if it were a sideways parabola instead then the axis of symmetry which actually be horizontal and be of the form y=a number.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: