Question

If the parent function f(x) = x2 is modified to g(x) = 2x2 + 1, which statement is true about g(x)?

Answer 1

If f(-x) = -f(x) that the function is odd. If  f(-x)=f(x) then the function is even.

g(-x) = 2(-x)^2+1 = 2x^2+1 = g(x). The function is even.
The answer to your question is A.
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Answer 2

The right answer is A. It is an even function.

A function is said to be even if its graph is symmetric with respect to the $y-axis$, that is:

$y=f(x) \ is \ \mathbf{even} \ if, \ for \ each \ x \ in \ the \ domain \ of \ f:\\ \\ f(-x)=f(x)$

Since:

$g(x)=2x^2+1 \ and \\ \\ g(-x)=2(-x)^2+1 \therefore g(-x)=2x^2+1 \\ \\ \therefore \boxed{g(x)=g(-x)}$