Use the image to answer the question.

Question

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 negative 2 left parenthesis x minus 4 right parenthesis squared plus 8

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 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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Answer 1

To determine the vertex form of the parabola based on the information provided, we focus on the standard vertex form of a parabola, which is given by:

\[ y = a(x - h)^2 + k \]

where \((h, k)\) is the vertex of the parabola, and \(a\) indicates the direction and width of the parabola.

1. Identify the Vertex: Since the specific point and position of the vertex are not shown in the question, you can look for hints in the answer choices. The vertex appears to be at \( (4, 8) \) based on the provided choices.

2. Check the Orientation and Width of the Parabola: The parabola is reported to open upward, which means \(a\) should be positive. Given that there are two options with \(a=2\) and one option with \(a=-2\), we can eliminate the negative option.

3. Last Check for the Coordinates: The vertex appears to be at coordinates \((4, 8)\). The only choice that reflects this is:

   \[ y = 2(x - 4)^2 + 8 \]

This expression should represent an upward-opening parabola with a vertex at \( (4, 8) \).

Therefore, the correct vertex form of the graphed equation is:

y = 2(x − 4)² + 8.