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Solve the equation y = 2(x - 2)^2 - 2 using the vertex form.

a) y = 2(x - 2)^2 - 2
b) y = 2x^2 - 8x + 8
c) y = 2x^2 - 4x + 2
d) y = 2x^2 - 4x - 6

User Inversus
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1 Answer

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Final Answer:

The equation y = 2(x - 2)^2 - 2 written in vertex form is:

y = 2(x - 2)^2 - 2 Option A is answer.

Step-by-step explanation:

The standard vertex form for a parabola is:

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

where:

a controls the shape of the parabola (stretching or compressing)

h is the x-coordinate of the vertex

k is the y-coordinate of the vertex

Given the equation:

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

we can identify the following:

a = 2 (stretches the parabola vertically)

h = 2 (moves the vertex to the right 2 units)

k = -2 (moves the vertex down 2 units)

Therefore, the equation is already written in vertex form.

Here are the other options:

b) y = 2x^2 - 8x + 8: This is not in vertex form because it doesn't have the squared term isolated.

c) y = 2x^2 - 4x + 2: This is not in vertex form because it doesn't complete the square.

d) y = 2x^2 - 4x - 6: This is not in vertex form because it doesn't complete the square and the vertex is not at (2, -2).

Option A is answer.

User Meirion Hughes
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