1. **State the problem:** Find the x-intercepts of the quadratic function given by $$y = x^2 - 2x - 15$$. 2. **Recall the formula:** The x-intercepts occur where $$y = 0$$, so solve the quadratic equation $$x^2 - 2x - 15 = 0$$. 3. **Use the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the roots are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 4. **Identify coefficients:** Here, $$a = 1$$, $$b = -2$$, and $$c = -15$$. 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = (-2)^2 - 4(1)(-15) = 4 + 60 = 64$$. 6. **Find the roots:** $$x = \frac{-(-2) \pm \sqrt{64}}{2(1)} = \frac{2 \pm 8}{2}$$. 7. **Calculate each root:** - $$x_1 = \frac{2 + 8}{2} = \frac{10}{2} = 5$$ - $$x_2 = \frac{2 - 8}{2} = \frac{-6}{2} = -3$$ 8. **Conclusion:** The x-intercepts of the graph are $$x = 5$$ and $$x = -3$$.