
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
You collect data on the number of hours studied $(x)$ and resulting test scores $(y)$ for three students and obtain the points $(x_{1}, y_{1}) = (1, y_1), (x_{2}, y_{2}) = (2, y_2), (x_{3}, y_{3}) = (3, y_3)$. If one wants to fit this data using a quadratic equation of the form $y = ax^2 + bx + c$, what is the value of $a$ in the best quadratic fit for these data points?
A) $\frac{y_2 - y_1}{2}$
B) $\frac{y_3 - 2y_2 + y_1}{2}$
C) $\frac{y_3 - y_1}{2}$
D) $\frac{y_3 - y_1}{6}$
E) None of these

Present the answer in LaTex format: \boxed{Your answer}
user