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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 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
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Answer 1

To determine the vertex form of the approximated graphed equation of the parabola, we need to know the vertex coordinates from the coordinate plane. 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 \( a \) indicates the direction and width of the parabola.

From the context you provided, it seems like an upward-opening parabola which means \( a \) will be positive. Based on the options given, we will want to find the correct values of \( h \) and \( k \) corresponding to the vertex.

Given the options:

1. \( y = -2(x - 4)^2 + 8 \) (downward opening)
2. \( y = 2(x - 4)^2 + 8 \) (upward opening)
3. \( y = 2(x + 4)^2 + 8 \) (upward opening, but with a different vertex)
4. \( y = 2(x - 4)^2 - 8 \) (upward opening, but with a different vertex)

Assuming the vertex on the parabola is at the coordinate (4, 8), since the parabola opens upwards, the correct form would be:

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

Thus, the correct response is:

y=2(x−4)2+8.