Question

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 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 minus 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's equation, we typically look for the vertex coordinates and the direction the parabola opens.

1. **Vertex Form of a Parabola**: The vertex form of a parabola is given by the equation \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex of the parabola and \(a\) determines the direction and width of the parabola.

2. **Vertex Coordinates**: In your description, the vertex appears to be at the point (4, 8), which suggests \(h = 4\) and \(k = 8\).

3. **Direction**: The parabola opens upwards, which means the coefficient \(a\) should be positive.

Given these points:
- The vertex is at (4, 8).
- Since the parabola opens upwards, \(a\) should be positive.

Now let's evaluate the provided equations:

- \(y = -2(x - 4)^2 + 8\) (downward opening, incorrect)
- \(y = 2(x + 4)^2 + 8\) (vertex not at (4,8), incorrect)
- \(y = 2(x - 4)^2 - 8\) (vertex not at (4,8), incorrect)
- \(y = 2(x - 4)^2 + 8\) (correct vertex at (4,8), upwards opening)

Based on this evaluation, the correct answer is:

**y = 2(x - 4)^2 + 8**.