Question

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

Answer 1

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.