Answer:
a) The portfolio will be at maximum after 12 months (1 year)
b) The maximum value of the portfolio is $5432
Step-by-step explanation:
The function that models Jennifer's stock portfolio (in dollars) is [tex]f(t)=-3t^2+72t+5000[/tex], where t is the time in months since she opened the account.
We complete the square to obtain this function in vertex form:
Factor -3 from the first two terms
[tex]f(t)=-3(t^2-24t)+5000[/tex].
Add the zero pairs -3(+144),-3(-144)
[tex]f(t)=-3(t^2-24t+144)+5000+-3(-144)[/tex].
Factor the perfect square trinomial and simplify.
[tex]f(t)=-3(t-12)^2+5432[/tex].
The vertex of this function is (h,k)=(12,5432)
a) The portfolio will be at maximum when t=12, the h-value of the vertex
b) The maximum value of the portfolio is the k-value of the vertex which is 5432
