Chapter 3 - Quadratic Functions - 3.2 The Vertex of a Parabola - Exercises and Problems for Section 3.2 - Exercises and Problems - Page 128: 38

$f(x)=-(x-1)^2+4$

Yes, we can find such a function. The vertex is $(1,4)$, so $$f(x)=a(x-1)^2+4$$ for some $a$. To find $a$, we use the fact that $x=-1$ is a zero, that is, the fact that $f(-1)=0$. We have $$f(-1)=a(-1-1)^2+4=0$$, so $$4 a+4=0$$ and $$a=-1$$. Thus $$f(x)=-(x-1)^2+4.$$