1. We are asked to determine certain key features of the quadratic function $f(x)$. 2. The vertex form of a quadratic function $f(x) = ax^2 + bx + c$ is given by the vertex coordinates $\left(\frac{-b}{2a}, f\left(\frac{-b}{2a}\right)\right)$. 3. From previous work (not shown here), let's assume $f(x) = ax^2 + bx + c$ with known $a$, $b$, and $c$. The vertex x-coordinate is $x_v=\frac{-b}{2a}$. Substitute $x_v$ back into $f(x)$ to get $y_v=f(x_v)$. 4. i) The vertex coordinates are $\left(x_v, y_v\right)$. 5. ii) Since $a>0$, the parabola opens upwards, so the vertex is a minimum; if $a<0$, it opens downwards and vertex is a maximum. The minimum or maximum value is $y_v$. 6. iii) The axis of symmetry is the vertical line passing through the vertex: $x=\frac{-b}{2a}$. 7. iv) The y-intercept is found by evaluating $f(0)=c$. These steps provide the answer to all four requested parts based on the quadratic function.