Answer:
Observe attached image
Function zeros:
(3, 0), (5, 0)
Vertex:
(4, 2)
Axis of symmetry:

Explanation:
First factorize the function

Take -2 as a common factor.

Now factor the expression

You must find two numbers that when you add them, obtain the result -8 and multiplying those numbers results in 15.
These numbers are -5 and -3
Then we can factor the expression in the following way:

The quadratic function cuts the x-axis at x = 3 and at x = 5.
Now we find the coordinates of the vertex.
For a function of the form
the x coordinate of its vertex is:

In the function


Then the vertice is:

The y coordinate of the symmetry axis is

The axis of symmetry is a vertical line that cuts the parabola in two equal halves. This axis of symmetry always passes through the vertex.
Then the axis of symmetry is the line

The solutions and the vertice written as ordered pairs are:
Function zeros:
(3, 0), (5, 0)
Vertex:
(4, 2)