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.