Chapter 3 - Quadratic Functions - 3.2 The Vertex of a Parabola - Exercises and Problems for Section 3.2 - Exercises and Problems - Page 128: 29

$ y=-3(x-2)^2+5 $

Using the vertex form $y=a(x-h)^2+k$, we know that $(h, k)=(2,5)$. We have $$ y=a(x-2)^2+5 $$ We use the point $(1,2)$ to find the value of $a$. $$ \begin{aligned} a(1-2)^2+5 & =2 \\ a & =-3 \\ \end{aligned} $$ Hence, $$ y=-3(x-2)^2+5 $$