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

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

m(x)=25x2

1 answer

To relate the square root function \( k(x) = \sqrt{5}x \) to the associated quadratic function, we need to find the function that represents the square of the original function.

If \( k(x) = \sqrt{5}x \), then squaring both sides gives:

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

Therefore, the corresponding quadratic function \( m(x) \) is:

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

Based on your options, the correct identification of the quadratic function related to the square root function \( k(x) = \sqrt{5}x \) is:

m(x) = 5x².