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 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

y=−2(x−4)2+8

Answer 1

To determine the vertex form of the graphed equation of the parabola, we need to identify the vertex and the value of "a" (the coefficient that describes the width and direction of the parabola).

In vertex form, the equation is expressed as:

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

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

1. Identify the vertex:

   • If the vertex appears to be at coordinates \((4, 8)\), then \(h = 4\) and \(k = 8\).

2. Identify the value of "a":

   • Since the parabola opens upward, "a" is positive.
   • If we determine that the parabola opens, for example, with a vertical stretch, we could assume that \(a = 2\).

Given these observations, the vertex form of the equation can be expressed as:

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

Since the vertex appears to match these coordinates, the correct response is:

y = 2(x - 4)² + 8