Question
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A coordinate plane shows an upward-opening parabola with a plotted point. Both axes range from negative 20 to 20 in increments of 5.
What is the vertex form of the graphed equation?
(1 point)
Responses
y=2(x−4)2−8
y equals 2 left parenthesis x minus 4 right parenthesis squared minus 8
y=−2(x−4)2+8
y equals negative 2 left parenthesis x minus 4 right parenthesis squared plus 8
y=2(x+4)2+8
y equals 2 left parenthesis x plus 4 right parenthesis squared plus 8
y=2(x−4)2+8
y equals 2 left parenthesis x minus 4 right parenthesis squared plus 8
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A coordinate plane shows an upward-opening parabola with a plotted point. Both axes range from negative 20 to 20 in increments of 5.
What is the vertex form of the graphed equation?
(1 point)
Responses
y=2(x−4)2−8
y equals 2 left parenthesis x minus 4 right parenthesis squared minus 8
y=−2(x−4)2+8
y equals negative 2 left parenthesis x minus 4 right parenthesis squared plus 8
y=2(x+4)2+8
y equals 2 left parenthesis x plus 4 right parenthesis squared plus 8
y=2(x−4)2+8
y equals 2 left parenthesis x minus 4 right parenthesis squared plus 8
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine the vertex form of the given parabola, we should identify the vertex and the direction of opening (upward or downward) based on the plotted point.
Since the parabola opens upward and assuming that the vertex is at (4, -8) (from the first option, for example), the vertex form of a parabola is represented as:
\[ y = a(x - h)^2 + k \]
Where:
- \( (h, k) \) is the vertex of the parabola.
- \( a \) determines the width and direction of the opening.
Assuming the plotted point on the graph indicates the vertex as (4, -8) and the parabola opens upwards, the equation would be:
\[ y = a(x - 4)^2 - 8 \]
From the response options provided:
- If \( a = 2 \), the equation becomes \( y = 2(x - 4)^2 - 8 \).
Therefore, the correct answer is:
**y = 2(x−4)²−8** (the first option).
Since the parabola opens upward and assuming that the vertex is at (4, -8) (from the first option, for example), the vertex form of a parabola is represented as:
\[ y = a(x - h)^2 + k \]
Where:
- \( (h, k) \) is the vertex of the parabola.
- \( a \) determines the width and direction of the opening.
Assuming the plotted point on the graph indicates the vertex as (4, -8) and the parabola opens upwards, the equation would be:
\[ y = a(x - 4)^2 - 8 \]
From the response options provided:
- If \( a = 2 \), the equation becomes \( y = 2(x - 4)^2 - 8 \).
Therefore, the correct answer is:
**y = 2(x−4)²−8** (the first option).
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