Question

Which of the following correctly identifies the quadratic function that is related to the square root function k(x)=5x−−√
?(1 point)
Responses

m(x)=15x2
m left parenthesis x right parenthesis equals Start Fraction 1 over 5 End Fraction x squared

m(x)=5x2
m left parenthesis x right parenthesis equals 5 x squared

m(x)=125x2
m left parenthesis x right parenthesis equals Start Fraction 1 over 25 End Fraction x squared

m(x)=25x2

Answer 1

To find the quadratic function related to the square root function \( k(x) = 5\sqrt{x} \), we can express this in terms of the relationship between the square root function and its corresponding quadratic function.

Given the square root function, if we isolate \( x \), we can think of it as a square function in the following way:

1. Start with the function:
\[
k(x) = 5\sqrt{x}
\]

2. To find the corresponding quadratic function, we can square both sides:
\[
k(x)^2 = (5\sqrt{x})^2
\]
\[
m(x) = 25x
\]

However, none of the options presented corresponds directly to the expression \( m(x) = 25x \).

If we consider possible transformations without isolating \( k(x) \), we can recognize that one of the options must represent a transformation of the basic relationship \( y = x^2 \).

So, we will take a look again at the relationship:
- If \( k(x) = 5\sqrt{x} \) corresponds to squaring and yielding a parabola, then we'd consider the scaling factor due to the square root.

To summarize:
\[
k(x) = 5\sqrt{x} \implies m(x) = 25x
\]

From your choices, let's analyze them:

1. \( m(x) = \frac{1}{5}x^2 \) (not suitable)
2. \( m(x) = 5x^2 \) (also a quadratic, but does not relate directly)
3. \( m(x) = \frac{1}{25}x^2 \) (not suitable)
4. \( m(x) = 25x^2 \) (matches the form we derived).

Given the above analysis, the best match for a quadratic function corresponding to the square root function \( k(x) = 5\sqrt{x} \) is:

**\( m(x) = 25x \)**.
However, please check if the question might have been misinterpreted, since the form directly derived does not seem available. If you're looking for a transformation-based quadratic, \( m(x) = 25x^2 \) would be a conceivable evaluation for parabolic growth from our original square root function, although it oversimplifies direct correlation.

Please review to confirm the intentions behind options or context!