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The image shows a problem related to the properties of a parabola, given by the function \( f(x) = x^2 - 2x + 3 \). Let's break down the information:

- The equation of the parabola is \( f(x) = x^2 - 2x + 3 \), which is a quadratic function.
- The problem provides several properties of this parabola:
  1. The parabola opens **upwards** ("atas"), which is indicated by the positive coefficient of \( x^2 \) in the quadratic function.
  2. The axis of symmetry is on the **right** ("kanan") of the y-axis. This is determined by the vertex's x-coordinate.
  3. The parabola intersects the y-axis at the point \( (0, 3) \), which is found by evaluating \( f(0) = 3 \).
  4. The parabola **does not intersect the x-axis** ("tidak memotong sumbu x"), meaning it has no real roots (discriminant is negative).
  5. The graph has a **minimum** value of \( y = 2 \), which is the y-coordinate of the vertex.

### Explanation:
- **Opening Direction**: The parabola opens upwards because the coefficient of \( x^2 \) is positive.
- **Axis of Symmetry**: The formula for the axis of symmetry is \( x = -\frac{b}{2a} \), where \( a = 1 \) and \( b = -2 \). This gives \( x = 1 \), meaning the axis of symmetry is at \( x = 1 \), to the right of the y-axis.
- **Vertex**: The y-coordinate of the vertex is calculated by substituting \( x = 1 \) into the equation. \( f(1) = (1)^2 - 2(1) + 3 = 2 \), so the vertex is \( (1, 2) \).
- **Intersection with y-axis**: The y-intercept occurs at \( x = 0 \), giving \( f(0) = 3 \), so the point is \( (0, 3) \).
- **No x-axis intersection**: The discriminant \( \Delta = b^2 - 4ac \) is \( (-2)^2 - 4(1)(3) = 4 - 12 = -8 \), which is negative, indicating no real roots and no x-intercepts.
  
Would you like a detailed breakdown of any of these points?

### Related Questions:
1. How do we find the vertex of a parabola using its equation?
2. Why does the parabola open upwards in this case?
3. How can we determine whether a parabola has real roots?
4. What is the role of the discriminant in quadratic functions?
5. Can you explain how to find the axis of symmetry?

### Tip:
To determine the direction of a parabola's opening, always check the sign of the coefficient of \( x^2 \). A positive sign means the parabola opens upwards, and a negative sign means it opens downwards.

Diketahui parabola dengan persamaan f(x) = x^2 - 2x + 3. Jika diperhatikan, Parabola tersebut akan terbuka ke atas dengan sumbu simetri di sebelah kanan sumbu y. Parabola memotong sumbu y di (0, 3) dan parabola tidak memotong sumbu x. Grafik fungsi tersebut mempunyai nilai minimum y = 2.

Explore the properties of the quadratic function f(x) = x^2 - 2x + 3, including its direction, axis of symmetry, vertex, and intercepts. Learn how to determine the graph's minimum value and why it doesn't intersect the x-axis. Suitable for students in Grades 8-10.

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