adding a point in a manipulate command

Question

I am having trouble adding a point to mark the Min values of each parabola when using the Manipulate command?
Manipulate[
 Plot[x^2 - 2*(a - 2)*x + a - 2, {a, -20, 20}, 
  PlotRange -> {-200, 200}], {a, -10, 10}]

This gives me the parabolas but how do I get a vertex point visible as it moves with parameter a.

kglr · Accepted Answer

You can use the options MeshFunctions, Mesh and MeshStyle as follows:
Manipulate[Plot[x^2 - 2*(a - 2)*x + a - 2, {x, -20, 20}, 
  ClippingStyle -> False,
  MeshFunctions -> {# &}, 
  Mesh -> {{a - 2}}, 
  MeshStyle -> Directive[PointSize[Large], Red], 
  PlotRange -> {-200, 200}], {a, -10, 10}]

Alternatively, you can use Epilog
Manipulate[Plot[x^2 - 2*(a - 2)*x + a - 2, {x, -20, 20}, 
  Epilog -> {PointSize[Large], Red, Point[{a - 2, -6 + 5 a - a^2}]}, 
  PlotRange -> {-200, 200}], {a, -10, 10}]

where I have used the results from:
Minimize[x^2 - 2*(a - 2)*x + a - 2, x]

{-6 + 5 a - a^2, {x -> -2 + a}}

adding a point in a manipulate command

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