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For the quadratic function \( f(x) = x^2 - 2 \), the corresponding values for the input x and output f(x) are as follows:
X: -3 -2 -1 0 1 2 3
Y: 7 2 1 -2 -1 2 7
This quadratic function is in the form \( f(x) = x^2 - 2 \), which represents a parabolic curve opening upwards. The vertex of this parabola is at the point (0, -2), and the axis of symmetry is the vertical line through x = 0. The function has no real roots, as the vertex is below the x-axis. As x moves further from 0 in either direction, the function values increase symmetrically, with the vertex being the minimum value attained by the function.
The provided x-values of -3, -2, -1, 0, 1, 2, and 3 correspond to the y-values of 7, 2, 1, -2, -1, 2, and 7, respectively. These points lie symmetrically about the axis of symmetry at x = 0.
In conclusion, the quadratic function \( f(x) = x^2 - 2 \) exhibits a symmetrical parabolic curve opening upwards with a vertex at (0, -2) and no real roots. The symmetry and behavior of the function can be observed through the provided x-y values, showcasing the characteristic shape of a quadratic function.