To determine the vertex of a quadratic function that is related to the square root function plotted on the graph \( h(x) \), we need to analyze the typical properties of square root functions and their corresponding quadratic forms.
Square root functions, like \( y = \sqrt{x} \), have their vertex usually at the origin \( (0,0) \). When considering transformations (shifts, reflections, or scaling), the vertex of the corresponding quadratic function, which can be derived from the square root function, will also change accordingly.
In standard transformations, for example:
- \( y = a\sqrt{x - h} + k \) would shift the graph horizontally by \( h \) and vertically by \( k \).
Given the options provided, if the graph indicates a vertical shift up or down, the vertex would change accordingly.
Since you mentioned the vertex which might indicate a possible shift, please evaluate the positions:
- If the graph has been translated upwards and appears to be at the height of 2, then the vertex might be \( (0,2) \).
- If it has been translated downwards and is at -2, then the vertex would be \( (0,-2) \).
- Positive coordinates could denote shifts to the right (like \( (2,0) \)) or left towards \( (-2,0) \).
Without specific information about the transformations applied to the square root function you mentioned, I cannot definitively choose the correct vertex. However, if \( h(x) \) reflects a typical upward parabola originating from the vertex, I would check the graph for values presented.
Please analyze the graph of \( h(x) \) directly to check for the vertex location visually or mathematically depending on transformations applied to the square root function. If the vertex looks to be up 2 units, the correct choice would be \( (0, 2) \). If you found the vertex shift is downward, then likely, it could be \( (0, -2) \).
If you focus only on a specific transformation, more precise guidance could be given.
1 answer