Chapter 8 - Graphing Quadratic Functions - 8.2 - Graphing f(x) = ax^2 + c - Exercises - Page 429: 22

$x=\pm7$

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 $x$: $$f(x)=-x^2+49$$ $$-x^2+49=0$$ $$-x^2=-49$$ $$x^2=49$$ $$x=\pm\sqrt{49}=\pm7$$