To find the quadratic function related to the square root function \( k(x) = 5 \sqrt{x} \), we start by expressing \( k(x) \) in terms of \( y \):
\[ y = 5 \sqrt{x} \]
To convert this square root function into a quadratic function, we can square both sides of the equation to eliminate the square root:
\[ y^2 = (5 \sqrt{x})^2 \]
This simplifies to:
\[ y^2 = 25x \]
Now, we can rewrite this equation in the standard form of a quadratic function:
\[ x = \frac{1}{25}y^2 \]
This shows that the quadratic function related to the square root function \( k(x) = 5 \sqrt{x} \) is:
\[ x = \frac{1}{25}y^2 \]
Alternatively, you can express it in terms of \( y \) as a function of \( x \) (if that was your intent), resulting in:
\[ y^2 = 25x \]
For clarity, either of these forms can be viewed as a relationship involving a quadratic function derived from the given square root function.