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)
(
,
)
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)
(
,
)
Answers
GPT-4o mini
To find the vertex of the quadratic function that represents the inverse of a graphed square root function, we first need to understand the relationship between square root functions and their inverses.
A square root function in the standard form is typically expressed as:
\[
y = \sqrt{x}
\]
Its inverse can be found by swapping the \(x\) and \(y\) variables and solving for \(y\):
\[
x = \sqrt{y} \implies y = x^2
\]
The function \(y = x^2\) is a quadratic function. The vertex of this quadratic function occurs at the coordinate (0, 0), since it opens upwards and is symmetrical about the y-axis.
Therefore, the vertex of the related quadratic function representing the inverse of the square root function is:
\[
(0, 0)
\]
A square root function in the standard form is typically expressed as:
\[
y = \sqrt{x}
\]
Its inverse can be found by swapping the \(x\) and \(y\) variables and solving for \(y\):
\[
x = \sqrt{y} \implies y = x^2
\]
The function \(y = x^2\) is a quadratic function. The vertex of this quadratic function occurs at the coordinate (0, 0), since it opens upwards and is symmetrical about the y-axis.
Therefore, the vertex of the related quadratic function representing the inverse of the square root function is:
\[
(0, 0)
\]