1. **State the problem:** Match each quadratic equation with its corresponding graph based on the roots (x-intercepts). 2. **Recall the quadratic formula and factorization:** The roots of a quadratic $y = ax^2 + bx + c$ are the values of $x$ where $y=0$. These roots can be found by factoring or using the quadratic formula. 3. **Analyze each equation:** - For $y = x^2 - 3x + 2$: Factor: $$x^2 - 3x + 2 = (x - 1)(x - 2)$$ Roots: $x=1$ and $x=2$ - For $y = x^2 + 2x - 3$: Factor: $$x^2 + 2x - 3 = (x + 3)(x - 1)$$ Roots: $x=-3$ and $x=1$ - For $y = x^2 - 2x - 3$: Factor: $$x^2 - 2x - 3 = (x - 3)(x + 1)$$ Roots: $x=3$ and $x=-1$ 4. **Match with graphs:** - Top-left graph crosses x-axis near 1 and 2, so it matches $y = x^2 - 3x + 2$. - Top-right graph crosses x-axis near -3 and 1, so it matches $y = x^2 + 2x - 3$. - Bottom-center graph crosses x-axis near 0 and 3, but our roots are -1 and 3 for $y = x^2 - 2x - 3$. The closest match is this equation for the bottom-center graph. 5. **Final matching:** - Top-left: $y = x^2 - 3x + 2$ - Top-right: $y = x^2 + 2x - 3$ - Bottom-center: $y = x^2 - 2x - 3$