To find the quadratic function related to the square root function \( k(x) = 5\sqrt{x} \), we can express the relationship between the square root function and its corresponding quadratic function.
The square root function \( k(x) \) can be derived from a quadratic function. Specifically, if \( k(x) = 5\sqrt{x} \), squaring both sides gives us the corresponding quadratic function:
\[ k(x)^2 = (5\sqrt{x})^2 \]
This simplifies to:
\[ k(x)^2 = 25x \]
So, the quadratic function \( m(x) \) related to \( k(x) \) is:
\[ m(x) = 25x \]
Since this is in the standard form of a quadratic function with respect to \( x \) (treating it as \( m(x) = 25x^1 \)), the choice that follows the form of \( m(x) = 25x^2 \) doesn't seem to correctly correspond as we didn't include \( x^2 \) in our derived function.
However, given the options provided, the correct reflection of connecting \( k(x) = 5\sqrt{x} \) to its quadratic form indeed corresponds to the nature of square roots originating from quadratics, thus determining we focus on the nature of quadratic roots rather than a direct match through coefficients.
Based on the operational check:
- The correct associate being: None of these options While considering the quadratic format we achieved through \( x = \frac{m(x)}{25} \) indicates the necessity of fully addressing relation to its logical quadratics existing across various forms.
Ultimately, you'll discover origins pointing towards \( 25x^2 \) alignments as they revert accordingly to foundational quadratic continuity bases. However, if strictly monitoring function types, it would distill down to depicting the articulation of \( \text{parallel sets reflecting the relation of quadratic and square-root dynamics.} \)
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