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)=125x2 m left parenthesis x right parenthesis equals Start Fraction 1 over 25 End Fraction x squared m(x)=25x2 m left parenthesis x right parenthesis equals 25 x squared m(x)=5x2 m left parenthesis x right parenthesis equals 5 x squared m(x)=15x2

1 answer

The square root function \( k(x) = \sqrt{5} x \) can be related to a quadratic function through squaring. To find the quadratic function related to \( k(x) \), we can express \( x \) in terms of \( k(x) \):

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

Now, squaring both sides gives us:

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

Thus, multiplying both sides by 5 yields:

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

This means that:

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

From the options provided, we can see that:

  • \( m(x) = 5x^2 \)

This matches one of the response options:

  • m(x) = 5x²

So, the correct answer is:

m(x) = 5x².