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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 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 vertex is 1,8

Answer 1

Given that the vertex of the parabola is at the point (4, -8), we can identify the equation in vertex form. The vertex form of a parabola is written as:

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

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

From the information provided:

• The vertex (h, k) is (4, -8).
• Since the parabola opens upwards, the value of "a" should be positive; based on the choices, it appears to be 2.

Therefore, substituting the values into the vertex form gives us:

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

Thus, the correct response is:

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