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

Answer 1

To determine the vertex form of the parabola graphed on the coordinate plane, we need to identify the vertex from the graph description.

The vertex form of a parabola is given by:

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

where \((h, k)\) is the vertex of the parabola.

From the responses provided, we can see different vertex points and values of \(a\):

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

   • Vertex: \((4, 8)\), opening downward (since \(a < 0\))

2. \( y = 2(x - 4)^2 - 8 \)

   • Vertex: \((4, -8)\), opening upward

3. \( y = 2(x + 4)^2 + 8 \)

   • Vertex: \((-4, 8)\), opening upward

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

   • Vertex: \((4, 8)\), opening upward

Given that the parabola opens upward, the corresponding equations would involve \(a\) being positive. Thus, we are looking for options where \(a > 0\) and the vertex corresponds to \((4, 8)\) or \((4, -8)\).

Among the choices, the equation that corresponds to an upward-opening parabola with vertex \((4, 8)\) is:

y = 2(x - 4)² + 8

Therefore, the final answer is:

y = 2(x − 4)² + 8.