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.

b

step-by-step explanation: