1. **Problem 1: Analyze the quadratic function** $r(x) = x^2 + 2x - 35$. 2. **Check the vertex location:** The vertex of a parabola $y = ax^2 + bx + c$ is at $x = -\frac{b}{2a}$. 3. For $r(x)$, $a=1$, $b=2$, so vertex $x$-coordinate is $-\frac{2}{2\times1} = -1$. 4. Since the vertex $x$-coordinate is $-1$, the vertex is not on the y-axis ($x=0$), so statement #1 is incorrect. 5. **Find zeros:** Solve $x^2 + 2x - 35 = 0$. 6. Factor: $x^2 + 2x - 35 = (x + 7)(x - 5) = 0$. 7. Zeros are $x = -7$ and $x = 5$, so statement #2 is correct (contradicts the user's claim). 8. **Opening direction:** Since $a=1 > 0$, the parabola opens upward, so statement #3 is correct (contradicts the user's claim). --- 1. **Problem 2: Analyze the quadratic function** $p(x) = -3x^2 + 12x - 3$. 2. **Find vertex:** Vertex $x$-coordinate is $-\frac{b}{2a} = -\frac{12}{2\times(-3)} = 2$. 3. Calculate $p(2) = -3(2)^2 + 12(2) - 3 = -12 + 24 - 3 = 9$. 4. Vertex is at $(2, 9)$, so statement #1 is correct (contradicts the user's claim). 5. **Check point $(-1, -18)$:** Calculate $p(-1) = -3(-1)^2 + 12(-1) - 3 = -3 - 12 - 3 = -18$. 6. The point $(-1, -18)$ lies on the parabola, so statement #2 is correct (contradicts the user's claim). 7. **Check y-intercept:** At $x=0$, $p(0) = -3(0)^2 + 12(0) - 3 = -3$. 8. The y-intercept is $(0, -3)$, not $(0, -4)$, so statement #3 is incorrect. --- **Final conclusions:** - For $r(x)$: #1 is incorrect, #2 and #3 are correct. - For $p(x)$: #1 and #2 are correct, #3 is incorrect.