# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-7/1

Exercises: Try Out - Set 7: Real exam simulation to sharpen your skills and build confidence. - Problem 1

---

## Exercise 1

### Question

export const metadata = {
  title: "Problem 1",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

import { Graph } from "../graph";

Observe the curve below!

<Graph
  title="Parabola Graph"
  description={
    <span>
      A parabola intersecting the <InlineMath math="x" />-axis and the <InlineMath math="y" />-axis.
    </span>
  }
/>

The correct statements regarding the curve are

1. The intersection point of the curve with the <InlineMath math="x" />-axis is <InlineMath math="(4, 0)" />.
2. The intersection points of the curve with the <InlineMath math="y" />-axis are <InlineMath math="(0, -5)" /> and <InlineMath math="(0, 1)" />.
3. The axis of symmetry is <InlineMath math="y = -1" />.
4. The axis of symmetry is <InlineMath math="x = -3" />.


### Choices

- [ ] If $$(1)$$, $$(2)$$, and $$(3)$$ are correct.
- [x] If $$(1)$$ and $$(3)$$ are correct.
- [ ] If $$(2)$$ and $$(4)$$ are correct.
- [ ] If only $$(4)$$ is correct.
- [ ] If all are correct.

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 1",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/24/2025",
};

We will analyze each statement based on the given graph.

#### Analysis of Statement 1

Based on the graph, it is clear that the curve intersects the <InlineMath math="x" />-axis at the point <InlineMath math="(4, 0)" />.

Thus, statement <InlineMath math="(1)" /> is **correct**.

#### Analysis of Statement 2

Based on the graph, the curve intersects the <InlineMath math="y" />-axis at two points, namely at <InlineMath math="y = 3" /> and <InlineMath math="y = -5" />. So the intersection points are <InlineMath math="(0, 3)" /> and <InlineMath math="(0, -5)" />.

Statement <InlineMath math="(2)" /> states that the intersection points are <InlineMath math="(0, -5)" /> and <InlineMath math="(0, 1)" />. Since <InlineMath math="(0, 3) \neq (0, 1)" />, this statement does not match the graph.

Thus, statement <InlineMath math="(2)" /> is **incorrect**.

#### Analysis of Statement 3

The axis of symmetry for a horizontal parabola can be determined from the midpoint between the two <InlineMath math="y" />-intercepts (if known).

<MathContainer>
  <BlockMath math="y_p = \frac{y_1 + y_2}{2} = \frac{3 + (-5)}{2} = \frac{-2}{2} = -1" />
</MathContainer>

The axis of symmetry is obtained as the line <InlineMath math="y = -1" />.

Thus, statement <InlineMath math="(3)" /> is **correct**.

#### Analysis of Statement 4

Since the axis of symmetry is the horizontal line <InlineMath math="y = -1" />, the statement that the axis of symmetry is <InlineMath math="x = -3" /> (a vertical line) is clearly wrong.

Thus, statement <InlineMath math="(4)" /> is **incorrect**.

#### Conclusion

The correct statements are statements <InlineMath math="(1)" /> and <InlineMath math="(3)" />.


---
