1. **State the problem:** Find the zeros (roots) of the quadratic function given in vertex form: $$a(x-h)^2 + k = 0$$ 2. **Formula and rules:** The zeros of a quadratic are the values of $x$ that make the function equal to zero. Here, we set the expression equal to zero and solve for $x$. 3. **Isolate the squared term:** $$a(x-h)^2 + k = 0 \implies a(x-h)^2 = -k$$ 4. **Divide both sides by $a$ (assuming $a \neq 0$):** $$\cancel{a}(x-h)^2 = \frac{-k}{\cancel{a}} \implies (x-h)^2 = \frac{-k}{a}$$ 5. **Take the square root of both sides:** $$x - h = \pm \sqrt{\frac{-k}{a}}$$ 6. **Solve for $x$:** $$x = h \pm \sqrt{\frac{-k}{a}}$$ 7. **Interpretation:** - If $\frac{-k}{a} \geq 0$, the zeros are real and given by the above formula. - If $\frac{-k}{a} < 0$, the zeros are complex (no real zeros). **Final answer:** $$\boxed{x = h \pm \sqrt{\frac{-k}{a}}}$$