1. **State the problem:** We are given the quadratic function $$y = (x - 1)(x - 3)$$ and asked to find the coordinates of the x-intercepts. 2. **Recall the formula and rules:** The x-intercepts occur where $$y = 0$$. For a quadratic in factored form $$y = (x - r_1)(x - r_2)$$, the x-intercepts are at $$x = r_1$$ and $$x = r_2$$. 3. **Find the x-intercepts:** Set $$y = 0$$: $$0 = (x - 1)(x - 3)$$ This product is zero if either factor is zero: $$x - 1 = 0 \quad \Rightarrow \quad x = 1$$ $$x - 3 = 0 \quad \Rightarrow \quad x = 3$$ 4. **Write the coordinates:** The x-intercepts are at points: $$(1, 0) \quad \text{and} \quad (3, 0)$$ 5. **Explanation:** The function crosses the x-axis at these points because the value of $$y$$ is zero there. The table values confirm this since $$y=0$$ at $$x=1$$ and $$x=3$$. 6. **Graph description:** The parabola opens upwards (since the coefficient of $$x^2$$ is positive when expanded). It passes through the points given, with minimum at $$x=2$$ where $$y=-1$$. Final answer: The x-intercepts are at $$(1, 0)$$ and $$(3, 0)$$.