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.