which of the following correctly identifies the quadratic function that is related to the square root function k (x) = 5 sq rt x ?

1 answer

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.