Question

Question

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

m(x)=5x^2
m left parenthesis x right parenthesis equals 5 x squared

m(x)=1/25x^2
m left parenthesis x right parenthesis equals Start Fraction 1 over 25 End Fraction x squared

m(x)=1/5x^2
m left parenthesis x right parenthesis equals Start Fraction 1 over 5 End Fraction x squared

m(x)=25x^2
m left parenthesis x right parenthesis equals 25 x squared
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Answer 1

To find the quadratic function related to the square root function \( k(x) = 5\sqrt{x} \), we can rewrite the square root function in terms of a quadratic function.

Recall that the square root function can be expressed as follows:

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

We can rewrite this in terms of a quadratic function by squaring both sides:

\[ k(x)^2 = (5\sqrt{x})^2 = 25x \]

This means that if \( m(x) \) is the corresponding quadratic function, we can express it as:

\[ m(x) = 25x \]

Since we are looking for a quadratic function \( m(x) \) that relates to the square root function \( k(x) \), we match it to the options provided. Notice that the form \( m(x) = 25x^2 \) corresponds to the representation of the quadratic function derived from the original square root function.

Thus, the correct answer is:

m(x) = 25x^2