Find the maximum value of y.

• Arc SR subtends $\angle STR$ and $\angle SQR$. Therefore, $\angle SQR = \angle STR = 25^\circ$.
• Arc RT subtends $\angle RST$ and $\angle RQT$. Therefore, $\angle RQT = \angle RST = 45^\circ$.

From the diagram, $\angle RQT = \angle RQS + \angle SQT$.

Arc ST subtends $\angle SRT$ and $\angle SQT$. So, $\angle SRT = \angle SQT = 20^\circ$.
In $\triangle RST$, the sum of angles is $\angle RST + \angle STR + \angle SRT = 45^\circ + 25^\circ + 20^\circ = 90^\circ$.
This sum is not $180^\circ$, indicating an inconsistency in the problem statement's given values.

Given the inconsistency, the question as stated cannot be solved to yield a valid geometric configuration. However, in multiple-choice questions with such flaws, it is common for one of the options to correspond to a related, correctly calculable angle. The value $\angle SQT = 20^\circ$ is derivable and matches option C. It is highly probable that the question intended to ask for $\angle SQT$ instead of $\angle STQ$, or there is a typo in the given angles. If $\angle STQ$ were $20^\circ$, it would imply $\angle RTQ = -5^\circ$, which is impossible. Therefore, assuming a typo in the question asking for $\angle SQT$ is the most reasonable path to an answer from the options.

The most plausible answer, assuming a typo in the question and it meant to ask for $\angle SQT$, is $\boxed{20^\circ}$.

The graph shows a parabola opening upwards. For such a parabola, the minimum value of y occurs at its vertex (the lowest point).

By observing the graph, the lowest point of the parabola is at the coordinates $x = -1$ and $y = -4$.

The minimum value of y is the y-coordinate of the vertex.
From the graph, the minimum value of y is $-4$.

The minimum value of y is $\boxed{-4}$.