Question

Find the related square root function, p(x), for the quadratic equation h(x)=4x^2 with he domain of (0, infinity).
p(x)=square root of ax where a=

Answer 1

To find the related square root function \( p(x) \) for the quadratic equation \( h(x) = 4x^2 \) with a domain of \( (0, \infty) \), we can express \( p(x) \) in terms of \( h(x) \).

Since we are looking for a square root function, we can take the square root of \( h(x) \):

\[
p(x) = \sqrt{h(x)} = \sqrt{4x^2}
\]

Simplifying this, we get:

\[
p(x) = \sqrt{4} \cdot \sqrt{x^2} = 2x
\]

So, we can express \( p(x) \) in terms of the form \( \sqrt{ax} \).

To match the form \( p(x) = \sqrt{ax} \), notice that \( p(x) = 2x \) can be rewritten as:

\[
p(x) = \sqrt{(2^2)(x^2)} = \sqrt{4x^2}
\]

In this case, \( a = 4 \).

Therefore, the answer is:

\[
a = 4
\]