1. **State the problem:** Solve the quadratic equation by graphing and finding its zeros: $$x^2 + 4x = 5$$ 2. **Rewrite the equation in standard form:** Move all terms to one side to set the equation equal to zero: $$x^2 + 4x - 5 = 0$$ 3. **Identify the related function:** The function to graph is: $$f(x) = x^2 + 4x - 5$$ 4. **Find the zeros of the function:** To find the zeros, solve the quadratic equation: $$x^2 + 4x - 5 = 0$$ 5. **Use the quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=4$, and $c=-5$. 6. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 4^2 - 4 \times 1 \times (-5) = 16 + 20 = 36$$ 7. **Calculate the roots:** $$x = \frac{-4 \pm \sqrt{36}}{2 \times 1} = \frac{-4 \pm 6}{2}$$ 8. **Find each root:** - For the plus sign: $$x = \frac{-4 + 6}{2} = \frac{2}{2} = 1$$ - For the minus sign: $$x = \frac{-4 - 6}{2} = \frac{-10}{2} = -5$$ 9. **Interpretation:** The zeros of the function are $x = -5$ and $x = 1$, which are the points where the graph crosses the x-axis. **Final answer:** $$x = -5, \quad x = 1$$