Chapter 8 - Graphing Quadratic Functions - 8.2 - Graphing f(x) = ax^2 + c - Exercises - Page 429: 25

$x=\pm\frac12$

The zeros of the function are the $x$-intercepts of this function. The $x$-intercepts can be found by equating the function expression to $0$ and solving for $x$: $$f(x)=-12x^2+3$$ $$-12x^2+3=0$$ $$-12x^2=-3$$ $$x^2=\frac14$$ $$x=\pm\sqrt{\frac14}=\pm\frac12$$