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What is the vertex of the quadratic function that is related to the square root function in the graph? (1 point) Responses (0,−2) left parenthesis 0 comma negative 2 right parenthesis (−2,0) left parenthesis negative 2 comma 0 right parenthesis (0,2) left parenthesis 0 comma 2 right parenthesis (2,0) left parenthesis 2 comma 0 right parenthesis
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GPT-4o mini
To determine the vertex of a quadratic function that is related to a square root function, we need to recognize the relationship between quadratic functions and their vertex forms and how they can be derived from transformations of functions.
The standard form of a quadratic function is \( y = ax^2 + bx + c \), and its vertex can be found using the formula \( x = -\frac{b}{2a} \) to find the x-coordinate of the vertex, followed by substituting that x-value back into the function to find the y-coordinate.
However, since you are asking specifically about the vertex in relation to the square root function, we might look at a transformed function based on \( y = \sqrt{x} \).
From the options you've provided:
- (0,−2)
- (−2,0)
- (0,2)
- (2,0)
We can analyze these coordinates:
If we think of a function like \( y = a(\sqrt{x + h}) + k \), where the vertex translates to (h, k). For a related quadratic function (when squared), the vertex would imply where the function changes direction or its minimum/maximum value.
Among the choices provided, (0,−2) stands out if we consider it as a lower point in the y-axis.
If we take (0,−2) as a vertex of a quadratic equation (for instance, \( y = (x-0)^2 - 2 \)), the vertex lies at this coordinate.
Thus, the answer that represents the vertex related to the square root function is:
**(0,−2) (0 comma negative 2)**.
The standard form of a quadratic function is \( y = ax^2 + bx + c \), and its vertex can be found using the formula \( x = -\frac{b}{2a} \) to find the x-coordinate of the vertex, followed by substituting that x-value back into the function to find the y-coordinate.
However, since you are asking specifically about the vertex in relation to the square root function, we might look at a transformed function based on \( y = \sqrt{x} \).
From the options you've provided:
- (0,−2)
- (−2,0)
- (0,2)
- (2,0)
We can analyze these coordinates:
If we think of a function like \( y = a(\sqrt{x + h}) + k \), where the vertex translates to (h, k). For a related quadratic function (when squared), the vertex would imply where the function changes direction or its minimum/maximum value.
Among the choices provided, (0,−2) stands out if we consider it as a lower point in the y-axis.
If we take (0,−2) as a vertex of a quadratic equation (for instance, \( y = (x-0)^2 - 2 \)), the vertex lies at this coordinate.
Thus, the answer that represents the vertex related to the square root function is:
**(0,−2) (0 comma negative 2)**.
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