Asked by Jaz
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The graph of a parabola opening to the right is shown on coordinate grid with vertex at left-parenthesis negative 3 comma 1 right-parenthesis and focus at left-parenthesis negative 1 comma 1 right-parenthesis.
Question
Use the image to answer the question.
Write the standard form of the equation for the parabola shown in the graph.
(1 point)
Responses
left parenthesis y minus 1 right parenthesis squared equals 8 left parenthesis x plus 3 right parenthesis
Image with alt text: left parenthesis y minus 1 right parenthesis squared equals 8 left parenthesis x plus 3 right parenthesis
left parenthesis y minus 1 right parenthesis squared equals 2 left parenthesis x plus 3 right parenthesis
Image with alt text: left parenthesis y minus 1 right parenthesis squared equals 2 left parenthesis x plus 3 right parenthesis
left parenthesis x plus 3 right parenthesis squared equals 8 left parenthesis y minus 1 right parenthesis
Image with alt text: left parenthesis x plus 3 right parenthesis squared equals 8 left parenthesis y minus 1 right parenthesis
left parenthesis x plus 3 right parenthesis squared equals 2 left parenthesis y minus 1 right parenthesis
Image with alt text: left parenthesis x plus 3 right parenthesis squared equals 2 left parenthesis y minus 1 right parenthesis
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The graph of a parabola opening to the right is shown on coordinate grid with vertex at left-parenthesis negative 3 comma 1 right-parenthesis and focus at left-parenthesis negative 1 comma 1 right-parenthesis.
Question
Use the image to answer the question.
Write the standard form of the equation for the parabola shown in the graph.
(1 point)
Responses
left parenthesis y minus 1 right parenthesis squared equals 8 left parenthesis x plus 3 right parenthesis
Image with alt text: left parenthesis y minus 1 right parenthesis squared equals 8 left parenthesis x plus 3 right parenthesis
left parenthesis y minus 1 right parenthesis squared equals 2 left parenthesis x plus 3 right parenthesis
Image with alt text: left parenthesis y minus 1 right parenthesis squared equals 2 left parenthesis x plus 3 right parenthesis
left parenthesis x plus 3 right parenthesis squared equals 8 left parenthesis y minus 1 right parenthesis
Image with alt text: left parenthesis x plus 3 right parenthesis squared equals 8 left parenthesis y minus 1 right parenthesis
left parenthesis x plus 3 right parenthesis squared equals 2 left parenthesis y minus 1 right parenthesis
Image with alt text: left parenthesis x plus 3 right parenthesis squared equals 2 left parenthesis y minus 1 right parenthesis
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To write the standard form of the equation for the parabola, we can use the following information:
1. The vertex of the parabola is at \((-3, 1)\).
2. The focus of the parabola is at \((-1, 1)\), which means the parabola opens to the right.
The standard form for a horizontally opening parabola is given by:
\[
(y - k)^2 = 4p(x - h)
\]
where \((h, k)\) is the vertex and \(p\) is the distance from the vertex to the focus.
In this case:
- The vertex \((h, k) = (-3, 1)\)
- The focus is \((-1, 1)\), so the distance \(p\) from the vertex to the focus is \(2\) (since \(-1 - (-3) = 2\)).
Thus, \(4p = 4 \cdot 2 = 8\).
Now we can substitute the vertex coordinates and the value of \(4p\) into the standard form:
\[
(y - 1)^2 = 8(x + 3)
\]
Therefore, the correct equation of the parabola is:
\[
\boxed{(y - 1)^2 = 8(x + 3)}
\]
1. The vertex of the parabola is at \((-3, 1)\).
2. The focus of the parabola is at \((-1, 1)\), which means the parabola opens to the right.
The standard form for a horizontally opening parabola is given by:
\[
(y - k)^2 = 4p(x - h)
\]
where \((h, k)\) is the vertex and \(p\) is the distance from the vertex to the focus.
In this case:
- The vertex \((h, k) = (-3, 1)\)
- The focus is \((-1, 1)\), so the distance \(p\) from the vertex to the focus is \(2\) (since \(-1 - (-3) = 2\)).
Thus, \(4p = 4 \cdot 2 = 8\).
Now we can substitute the vertex coordinates and the value of \(4p\) into the standard form:
\[
(y - 1)^2 = 8(x + 3)
\]
Therefore, the correct equation of the parabola is:
\[
\boxed{(y - 1)^2 = 8(x + 3)}
\]
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