Magtanong at makakuha ng malinaw na mga sagot sa IDNStudy.com. Makakuha ng mga kumpletong sagot sa lahat ng iyong mga tanong mula sa aming network ng mga eksperto.
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.