Chapter 5 - Exponential and Logarithmic Functions - 5.3 Exponential Functions - 5.3 Assess Your Understanding - Page 285: 138

$f(x)=-2(x-3)^2+5=-2x^2+12x-13$

Step 1. Assume the function has the form of $f(x)=a(x-h)^2+k$ Step 2. Given the vertex at $(3,5)$, we have $h=3, k=5$ Step 3. With the point $(2,3)$ of the function, we have $f(2)=a(2-3)^2+5=3$, thus $a=-2$ Step 4. Thus $f(x)=-2(x-3)^2+5=-2x^2+12x-13$