1. The problem asks to identify the values of $a$ and $b$ in the quadratic function. 2. A quadratic function is generally written as $y = ax^2 + bx + c$. 3. The vertex form is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex. 4. Given the vertex $(3, 8)$ and axis of symmetry $x=3$, the vertex form is $y = a(x - 3)^2 + 8$. 5. Without additional points or information, $a$ and $b$ cannot be uniquely determined. 6. However, from the vertex form, $b$ relates to $a$ and $h$ by $b = -2ah$. 7. Since $h=3$, $b = -6a$. 8. So $a$ is unknown and $b$ depends on $a$ as $b = -6a$. 9. More information is needed to find exact values of $a$ and $b$.