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)=25x2 m left parenthesis x right parenthesis equals 25 x squared 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

Answer 1

To identify the quadratic function related to the square root function \( k(x) = \sqrt{5}x \), we need to consider the relationship between a square root function and its corresponding quadratic function.

The square root function can be rewritten as:

\[ k(x) = \sqrt{5}x \implies k(x)^2 = 5x \]

To find the related quadratic function, we square both sides:

\[ y = k(x) \implies y^2 = 5x \]

This implies that the quadratic function related to \( k(x) \) can be expressed as \( m(x) = 5x^2 \) when we express \( x \) in terms of \( y \), indicating that we are dealing with quadratic functions derived from the square root.

Now we check the given options:

1. \( m(x) = 25x^2 \)
2. \( m(x) = 15x^2 \)
3. \( m(x) = \frac{1}{5} x^2 \)
4. \( m(x) = 5x^2 \)
5. \( m(x) = 125x^2 \)

The correct identification is:

\[ m(x) = 5x^2 \]

Thus, the correct answer is:

\( m(x) = 5x^2 \).