Question

Use the image to answer the question.

A curve labeled g left parenthesis x right parenthesis is plotted in quadrant 1 of a coordinate plane.

Consider the quadratic function that represents the inverse of the graphed square root function. What would be the vertex of the related quadratic function?

(1 point)
(_,_)

Answer 1

To determine the vertex of the quadratic function that represents the inverse of the given square root function \( g(x) \), we need to understand the relationship between a function and its inverse.

The general form of a square root function is:

\[
g(x) = \sqrt{x}
\]

The inverse of this function can be found by switching the \( x \) and \( y \) in the equation:

\[
y = \sqrt{x} \implies x = \sqrt{y}
\]

To find the inverse function, we can square both sides:

\[
x^2 = y \implies y = x^2
\]

The inverse of the square root function \( g(x) = \sqrt{x} \) is \( g^{-1}(x) = x^2 \).

The quadratic function \( y = x^2 \) is in its standard form where the vertex is located at the point (0, 0). Therefore, the vertex of the associated quadratic function is:

\[
(0, 0)
\]

So the answer is:

(0, 0)