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Use the image to answer the 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 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 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 plus 8
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2 answers

To find the vertex form of a parabola, we look for the equation in the form \( y = a(x-h)^2 + k \), where \((h, k)\) is the vertex of the parabola.

Without the image, we can't determine the exact vertex or the value of \( a \). However, I can guide you through the options:

  1. Identify the vertex: Look for the coordinates of the vertex in the image. This will be represented as \((h, k)\).

  2. Determine the direction and stretch: The coefficient \( a \) indicates the direction and how narrow or wide the parabola is. If it's positive, it opens upwards; if it's negative, it opens downwards.

  3. Check points: If a specific point is plotted on the parabola in the image, ensure that point satisfies the equation you choose.

Assuming you have the vertex coordinates and the direction (which you can glean from the image), compare them to the options provided to find the correct vertex form.

For example, if the vertex is at (4, -8) and opens upwards with a value of 2 for \( a \), the equation would be \( y = 2(x-4)^2 - 8 \). Adjust similarly based on the vertex and the direction you observe.

Make sure to select the equation that matches the information derived from the image accurately.

the vertex is 4,8