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 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
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
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the vector is 4,8, not 4,-8, just 4,8.

Answer 1

Based on your description, the vertex of the parabola is at the point (4, 8). 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.

Since the vertex is (4, 8), we have h = 4 and k = 8. If the parabola opens upwards, 'a' is a positive value. From the options provided, we determine the correct form with 'a' as positive.

The correct equation matching these criteria is:

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

So the final answer is:

y=2(x−4)^2+8