Answer:
D. [tex]y = 2\cdot x^{2}-5[/tex]
Step-by-step explanation:
The given points show a symmetry that corresponds with a second-order polynomial (a parabola), that is:
[tex]y = A\cdot x^{2}+B\cdot x + C[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]A, B, C[/tex] - Coefficients.
Since the absolute minimum is associated with [tex]x = 0[/tex], then we infer the following conditions:
[tex]A > 0[/tex], [tex]B = 0[/tex], [tex]C = -5[/tex]
Therefore, the correct answer is D.
