1. **Stating the problem:** We are given three points (0, 3), (1, 0), and (3, 0) that define the boundary of a flower planting area. We need to determine which statements about the quadratic function describing this boundary are true. 2. **Finding the quadratic function:** Assume the quadratic function is $y = ax^2 + bx + c$. 3. **Using the points to find coefficients:** - At $x=0$, $y=3$ gives $c=3$. - At $x=1$, $y=0$ gives $a(1)^2 + b(1) + 3 = 0 \Rightarrow a + b + 3 = 0$. - At $x=3$, $y=0$ gives $9a + 3b + 3 = 0$. 4. **Solving the system:** From $a + b + 3 = 0$, we get $b = -a - 3$. Substitute into $9a + 3b + 3 = 0$: $$9a + 3(-a - 3) + 3 = 0$$ $$9a - 3a - 9 + 3 = 0$$ $$6a - 6 = 0$$ $$6a = 6$$ $$a = 1$$ Then $b = -1 - 3 = -4$. 5. **Quadratic function:** $$y = x^2 - 4x + 3$$ 6. **Check each statement:** - a. The function is $y = x^2 - 4x + 3$ (True). - b. Coefficient $a$ is 1, not -1 (False). - c. Axis of symmetry is $x = -\frac{b}{2a} = -\frac{-4}{2 \times 1} = 2$ (True). - d. Vertex coordinates: $$x = 2$$ $$y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1$$ So vertex is at $(2, -1)$ (True). - e. The parabola crosses the y-axis at $(0, 3)$ (True). **Final answers:** a, c, d, e are true; b is false.