To determine the vertex of the quadratic function related to a square root function, we first need to understand how a square root function is typically transformed into a quadratic function.
A square root function is generally expressed in the form: \( y = \sqrt{x} \)
To represent a quadratic function related to it, we can consider the function obtained by squaring both sides: \( y^2 = x \) or, \( x = y^2 \)
This is a parabola that opens to the right, with its vertex at the point (0,0).
If there are any transformations involved (translations, etc.), we would need more specific information or a graphical representation to determine the exact vertex of the related quadratic function.
Since you provided possible vertex points:
- (0, −2)
- (−2, 0)
- (2, 0)
- (0, 2)
Assuming the common quadratic transformations don't result in any shifts or that we aren't given further details about shifts, the original vertex remains (0, 0). However, since (0, 0) isn't among the options, you could be looking for the vertex of a shifted function.
If we were to measure typical parabolic shifts, we might eventually deduce that the "related" quadratic function could have been shifted downward or translated, yielding options like (0, −2) if it had been downward shifted by 2 units.
Based on your options and typical transformations, the closest vertex responding to a downward shift would be:
(0, −2)
So, the answer is: (0, −2)
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