1. **Stating the problem**: We have a quadratic function $f(x) = ax^2 + bx + c$, with a parabola opening downward and vertex near $(-1, \text{max value})$, crossing the y-axis at $(0,10)$ and going through the point $(3,10)$. We want to determine the maximum value of $f(x)$ and check if given statements (1) and (2) are sufficient to find it. 2. From statement (2), because $f(0) = c = 10$, we know $c=10$. 3. From statement (1), $f(3) = 9a + 3b + c = 10$, substituting $c=10$ gives: $$9a + 3b + 10 = 10 \implies 9a + 3b = 0 \implies 3a + b = 0 \implies b = -3a$$ 4. The parabola opens downward, so $a<0$, and the vertex x-coordinate is given by: $$x_v = -\frac{b}{2a} = -\frac{-3a}{2a} = \frac{3}{2} = 1.5$$ 5. The problem states vertex near $x=-1$, but our calculation from the two points gives $x_v=1.5$. This suggests the exact vertex position is uncertain with the two statements. 6. The maximum value is $f(x_v) = a x_v^{2} + b x_v + c$. Using $b=-3a$ and $c=10$: \begin{align*} f(1.5) &= a (1.5)^2 + (-3a)(1.5) + 10 \\ &= a (2.25) - 4.5 a + 10 = (2.25 - 4.5) a + 10 = -2.25 a + 10 \end{align*} 7. Since $a$ is unknown, maximum value depends on $a$, which is not determined uniquely by (1) and (2). 8. Conclusion about sufficiency of statements: - Statement (1) alone: Knowing $f(3)=10$ only gives one equation with $a,b,c$ unknown. - Statement (2) alone: Knowing $f(0)=10$ only gives $c=10$. - Together: we find $b = -3a$ and $c=10$, but $a$ is still unknown, so maximum value cannot be uniquely found. Hence, answer is **E**: statements (1) and (2) are not sufficient to answer the question about maximum value. **Final answer:** E Pernyataan (1) dan pernyataan (2) tidak cukup untuk menjawab pertanyaan