This post is under Algebra so we should assume that the OP does not know any calculus.You are told the numerical coordinates of the minimum point,
this gives you two pieces of information
1.) when the x co-ord of the minimum point is input into the derivative of the curve's function, it maps to a 0 [by definition]
2.)when the x co-ord of the minimum point is input into the function it outputs a -6.
How can you use this information to reach the goal of determining the values of a and k
The OP doing is a questionThis post is under Algebra so we should assume that the OP does not know any calculus.
The given min helps you find a as well as the period. That is all you need to find a and kThe OP doing is a question
the where the phrase is used "local minimum point" i think not a pre calculus student can
find this useful
hence, OP knows calculus
Q.E.D