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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 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

y=2(x−4)2−8

1 answer

To determine the vertex form of the graphed equation of the upward-opening parabola, we would look for the vertex of the parabola.

In vertex form, the equation is represented as:

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

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

Since I don't have the image to reference, here’s how you can analyze the options based on the vertex:

  1. Identify the vertex from the graph. This will be the point \((h, k)\).
  2. Determine whether the parabola opens upward or downward to find the sign of \(a\):
    • If it opens upward, \(a > 0\).
    • If it opens downward, \(a < 0\).
  3. Check the correct choice based on the vertex and the value of \(a\).

Once you analyze the graph and have the vertex \((h, k)\) and whether the parabola opens upward or downward, you can select the correct vertex form among the given choices.

For example:

  • If the vertex is at \((-4, 8)\) and it opens upward, the equation would be \(y = 2(x + 4)^2 + 8\).
  • If the vertex is at \((4, 8)\) and it opens upward, the equation would be \(y = 2(x - 4)^2 + 8\).

Without the visual, this is how you would select the correct response based on the key features of the parabola. Please analyze the graph and apply this reasoning to choose the correct option!