Question 1035300
Apply the changes one at a time.


Starting with {{{f(x)=4(x-0)^2+1}}}


Four units down
{{{4(x-0)^2+1-4}}}
{{{4(x-0)^2-3}}}


Five to the right
{{{4(x-5)^2-3}}}


Reflect across the x-axis
{{{(-1)(4(x-5)^2-3)}}}
{{{-4(x-5)^2+3}}}-----------new vertex  (5,3).



{{{graph(400,400,-2,8,-5,5,4x^2+1,-4(x-5)^2+3)}}}