Final answer:
The axis of symmetry for the given quadratic function f(x) = 2x^2 + 16x + 38 is x = -4.
Step-by-step explanation:
To determine the axis of symmetry of a quadratic function in standard form, we can use the formula x = -b/(2a). In the given quadratic function f(x) = 2x^2 + 16x + 38, the coefficient of x^2 is a = 2 and the coefficient of x is b = 16. Plugging these values into the formula, we get x = -16/(2*2) = -4.
Therefore, the axis of symmetry for the given quadratic function is x = -4.