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The given function is \( y = 3x^2 + 5x + 1 \), which is a quadratic function of the form \( y = ax^2 + bx + c \), where \( a = 3 \), \( b = 5 \), and \( c = 1 \). Let’s analyze its characteristics:

### 1. **Direction of the Parabola (Curve Opening)**
   Since \( a = 3 \), and it is positive, the parabola opens **upward**.

### 2. **Vertex of the Parabola**
   The x-coordinate of the vertex is given by the formula:
   \[
   x_{\text{vertex}} = \frac{-b}{2a} = \frac{-5}{2(3)} = \frac{-5}{6}.
   \]
   Since \( x_{\text{vertex}} = -\frac{5}{6} \), the vertex is on the **left** side of the y-axis.

### 3. **Y-intercept**
   The y-intercept is the value of \( y \) when \( x = 0 \), which is:
   \[
   y = 3(0)^2 + 5(0) + 1 = 1.
   \]
   Thus, the graph crosses the y-axis at \( y = 1 \).

### 4. **X-intercepts**
   To find the x-intercepts (where the graph crosses the x-axis), solve the quadratic equation:
   \[
   3x^2 + 5x + 1 = 0.
   \]
   Using the quadratic formula:
   \[
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-5 \pm \sqrt{5^2 - 4(3)(1)}}{2(3)} = \frac{-5 \pm \sqrt{25 - 12}}{6} = \frac{-5 \pm \sqrt{13}}{6}.
   \]
   Since the discriminant (\( \sqrt{13} \)) is positive, there are **two distinct real roots**, meaning the graph intersects the x-axis at **two distinct points**.

### Summary of the Characteristics:
- The vertex is to the left of the y-axis (i.e., "Titik puncak di **kiri** sumbu Y").
- The parabola opens **upward**.
- The graph crosses the x-axis at **two distinct points**.
- The graph crosses the y-axis above the x-axis (i.e., at \( y = 1 \)).

### Correct Answers:
- [ ] Titik puncak di kanan sumbu Y. (False, it's on the left.)
- [x] Kurva terbuka menghadap ke atas. (True, it opens upward.)
- [ ] Memotong sumbu Y di bawah sumbu X. (False, it intersects at \( y = 1 \), which is above the x-axis.)
- [x] Memotong sumbu X di dua titik berbeda. (True, it has two distinct x-intercepts.)

Would you like further details or explanations?

### Related Questions:
1. How do you determine if a parabola opens upward or downward?
2. How do you find the vertex of a quadratic function?
3. What does the discriminant of a quadratic equation indicate?
4. How can you tell if a parabola will intersect the x-axis at two points, one point, or not at all?
5. What is the significance of the y-intercept in a quadratic graph?

### Tip:
The discriminant (\( b^2 - 4ac \)) is key to determining the number of x-intercepts in a quadratic function.

Pangsa pasar sebuah produk mengalami kenaikan sedangkan barang tersebut mengalami kelangkaan. Sehingga fungsi penawaran barang tersebut menjadi y = 3x^2 + 5x + 1. Jika digambar grafiknya, maka manakah pernyataan berikut ini yang merupakan ciri-ciri grafik fungsi kuadrat tersebut?

Analyze the quadratic function y = 3x^2 + 5x + 1 to determine its graph characteristics, including the direction of the parabola, vertex position, and x-intercepts. This problem involves key concepts such as quadratic equations and discriminants. Suitable for students in Grades 9-11.

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