Find the minimum distance from a curve to a point not on it

[aeromat]

Homework Statement

You are given point (1,2).
f(x) = 0.199445983x^2 - 3.789473684x + 19
f'(x) = 0.398891966x - 3.789473684

You also know (0,19), (9.5,1) <-- this is the vertex.
This graph has the domain 0≤ x ≤ 9.5


Find the point on the curve that when joined to a line segment with this outside point (1,2), is the minimum distance that point could be away from the curve.

The Attempt at a Solution

I found out the equations myself because we were given a diagram, and the points as well. Now, I don't know how to proceed to get the minimum distance from the point to the curve..

 

[lanedance]

write the distance from (f(x),x) to (1,2) as a function of x and minimise

 

[aeromat]

Would you explain what you mean?