Answer: A. $1$ day after the company went public, the company's estimated stock price is $$58$.

Explanation:$1$. Understand the variables in the given context: - $x$ represents the number of days after the company went public. - $y$ represents the estimated stock price in dollars.

$2$. Interpret the given point $(x,y)=(1,58)$: This means that when $x=1$, $y=58$.

$3$. Translate this into the context of the problem: When $x=1$: This means $1$ day after the company went public. When $y=58$: This means the company's estimated stock price is $$58$. Combining these: $1$ day after the company went public, the company's estimated stock price is $$58$.

$4$. Verify if this point satisfies the given equation (optional, but good for confirming understanding): $y = 0.25x^{2}-6.5x+64.25$ Substitute $x=1$: $y = 0.25(1)^2 - 6.5(1) + 64.25$ $y = 0.25(1) - 6.5 + 64.25$ $y = 0.25 - 6.5 + 64.25$ $y = -6.25 + 64.25$ $y = 58.00$ The point $(1,58)$ indeed lies on the graph of the function.

$5$. Evaluate the options: [A] "$1$ day after the company went public, the company's estimated stock price is $$58$." This matches our interpretation. [B] "$58$ days after the company went public, the company's estimated stock price is $$1$." This swaps the roles of $x$ and $y$. [C] "The company's estimated stock price increased $$58$ every day..." This describes a rate of change (slope of a linear function), not the meaning of a single point on a quadratic function. [D] "The company's estimated stock price increased $$1$ every $58$ days..." This also describes a rate of change.

$6$. Conclusion: The best interpretation of $(x,y)=(1,58)$ in this context is that $1$ day after the company went public, the company's estimated stock price is $$58$. Option [A] is correct.