Question
A parabola is graphed on a coordinate plane. The x-axis ranges from negative 14 to 1 in increments of 1. The y-axis ranges from negative 2 to 6 in increments of 1.
Identify the vertex on the graph.
(1 point)
Responses
(−10,0)
left parenthesis negative 10 comma 0 right parenthesis
(−12,0)
left parenthesis negative 12 comma 0 right parenthesis
(−11,−1)
left parenthesis negative 11 comma negative 1 right parenthesis
x=−11
x equals negative 11
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Identify the vertex on the graph.
(1 point)
Responses
(−10,0)
left parenthesis negative 10 comma 0 right parenthesis
(−12,0)
left parenthesis negative 12 comma 0 right parenthesis
(−11,−1)
left parenthesis negative 11 comma negative 1 right parenthesis
x=−11
x equals negative 11
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Answers
Answered by
GPT-4o mini
To identify the vertex of the parabola, we need to know its specific characteristics from the given options. Unfortunately, the information provided does not include the equation of the parabola or a description of its shape. However, by looking at the options provided, we can make an educated guess.
In general, the vertex of a parabola represented in the form \( y = ax^2 + bx + c \) can often be found at:
\[
x = -\frac{b}{2a}
\]
If we consider that the vertex is likely to be the highest or lowest point of the graph depending on whether the parabola opens upwards or downwards, we have:
- \( (−10,0) \)
- \( (−12,0) \)
- \( (−11,−1) \)
- \( x=−11 \)
Among those, the option \( (−11,−1) \) suggests that it may be the vertex if it represents a minimum point of a parabola opening upwards.
However, if we assume the shape of the parabola is symmetrical around \( x = -11\), and the y-values increase as we move away from it, then this point could indeed be the vertex.
Since we don't have the graph itself or additional information, it's safest to go with the most common representation of a vertex, which usually has a y-coordinate of zero for many parabolas on standard graphs.
Thus, the most reasonable vertex based on your options could be:
**(−11,−1)**
If it were known to be an opening-downward parabola, then this option may be the vertex as a maximum, confirming that the other points are below it. So **(−11,−1)** is a strong candidate for the vertex of the parabola in question.
In general, the vertex of a parabola represented in the form \( y = ax^2 + bx + c \) can often be found at:
\[
x = -\frac{b}{2a}
\]
If we consider that the vertex is likely to be the highest or lowest point of the graph depending on whether the parabola opens upwards or downwards, we have:
- \( (−10,0) \)
- \( (−12,0) \)
- \( (−11,−1) \)
- \( x=−11 \)
Among those, the option \( (−11,−1) \) suggests that it may be the vertex if it represents a minimum point of a parabola opening upwards.
However, if we assume the shape of the parabola is symmetrical around \( x = -11\), and the y-values increase as we move away from it, then this point could indeed be the vertex.
Since we don't have the graph itself or additional information, it's safest to go with the most common representation of a vertex, which usually has a y-coordinate of zero for many parabolas on standard graphs.
Thus, the most reasonable vertex based on your options could be:
**(−11,−1)**
If it were known to be an opening-downward parabola, then this option may be the vertex as a maximum, confirming that the other points are below it. So **(−11,−1)** is a strong candidate for the vertex of the parabola in question.