Question 868307
{{{f(x)=-5(x^2-(4/5)x+3/5)}}}
{{{f(x)=-5(x^2-(4/5)x+(2/5)^2+3/5-(2/5)^2)}}}, completing the square
{{{f(x)=-5((x-2/5)^2+(3/5-4/25))}}}
{{{f(x)=-5((x-2/5)^2+(15/25-4/25))}}}
{{{f(x)=-5((x-2/5)^2+11/25)}}}
Distribute the factor over the sum.
{{{highlight(f(x)=-5(x-2/5)^2-11/5)}}}, in essence, in the form you wanted.


Question parts (a) and (b) are about the vertex.
Vertex is (2/5, -11/5).