Answer: option C.
Step-by-step explanation:
Given a quadratic function of the form [tex]ax^2+bx+c[/tex], if the coefficient a is less than zero, then the function is opened upward.
The options A is not opened upwards, then it is not the answer.
Then the given equation [tex]x^2+2=6[/tex] can be written as:
[tex]x^2+2-6=0\\x^2-4=0[/tex]
This function is equal to the parent function, shifted 4 units down.
Therefore, the graph that you are looking for must be a parabola that is opened upwards and has its vertex in the point (0,-4).
Then, the correct option is C. And the solution is:
[tex]x=-2\\x=2[/tex]
