Finding the Axis of Symmetry: Solve for Symmetry in f(x) = 4x^2 + 6

To find the axis of symmetry for the quadratic function $f(x) = 4x^2 + 6$, we employ the formula for the axis of symmetry of a parabola given by $ax^2 + bx + c$, which is $x = -\frac{b}{2a}$.

Given $f(x) = 4x^2 + 0x + 6$, we identify the coefficients from the function:

• $a = 4$
• $b = 0$

Substituting these values into the formula:

$x = -\frac{b}{2a} = -\frac{0}{2 \times 4} = 0$

Thus, the axis of symmetry for the quadratic function is $x = 0$.

Therefore, the solution to the problem is $\mathbf{x = 0}$.