Answer:
See the attachment for the points and line of interest.
Explanation:
A graphing calculator or graphing utility can show you the curve.
For ax²+bx+c, the line of symmetry is x=-b/(2a). That is also the x-coordinate of the vertex. The y-intercept is the constant, the value of the function when x=0. The x-intercepts are the values of x that make f(x) = 0.
Here, those are x=4 and x=-2. You can factor f(x) as (x+2)(x-4). These values of x make the factors, and the function, zero.