I have honestly no clue how to proceed with the above task. I know that the vertex is the lowest point of the graph, and by looking at this graph I'm assuming that the vertex is at the middle of it, which is when x = 10. I also know that r and s are the x and y coordinates of the vertex. I also know a bunch of other stuff like r = -b/2a, p+q = -b/a, p*q = c/a, but I have no idea how to begin solving this.
I tried by replacing r by 10 and s by 1, but then I still have x and a which are unknown so I don't know what to do afterwards.
Maybe some of you can help guide me by asking me a leading question or something? If someone is willing to help me demistify all the random knowledge that I have on functions and maybe help me connect all the pieces together, I'd be very very grateful!
Hints:
A parabola's turning point occurs on its line of symmetry. (Why?)
$h(x)$ attains its minimum value when $(x-r)^2$ is minimised. (Why?)