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 plus 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

Answer 1

To determine the vertex form of the equation of the parabola, we need to identify the vertex and the direction in which the parabola opens (upward or downward).

1. Identify the vertex: 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. Since the parabola opens upward, the value of \(a\) is positive.

2. Analyzing the options:

   • For \(y = -2(x - 4)^2 + 8\), the parabola opens downward (because \(a\) is negative).
   • For \(y = 2(x + 4)^2 + 8\), the vertex is at \((-4, 8)\), but this would be incorrect if the vertex is at \((4, 8)\).
   • For \(y = 2(x - 4)^2 + 8\), the vertex is at \((4, 8)\) and the parabola opens upward.
   • For \(y = 2(x - 4)^2 - 8\), the vertex would be at \((4, -8)\), which doesn't fit if the vertex is at \((4, 8)\).

So, if the vertex of the graph is at the point \((4, 8)\) and the parabola opens upward, the correct answer is:

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