Final Answer:
The function of a parabola whose vertex is on the x-axis depends on the direction it opens. If it opens upwards, the vertex is the minimum point of the parabola. If it opens downwards, the vertex serves as the maximum point.
Step-by-step explanation:
When the vertex of a parabola is on the x-axis, its general form is given by
where (h, k) represents the coordinates of the vertex. The coefficient 'a' determines the direction of the parabola. If 'a' is positive, the parabola opens upwards, and if 'a' is negative, the parabola opens downwards.
In the case of an upward-opening parabola, the vertex, which is the minimum point, lies on the x-axis. This implies that the value of 'k' is the minimum value of the function.
Conversely, for a downward-opening parabola, the vertex is the maximum point on the x-axis, indicating that 'k' represents the maximum value of the function. These relationships are crucial when analyzing the behavior of the parabola in various mathematical contexts.
Understanding the orientation of a parabola is essential for solving real-world problems and mathematical applications. Whether modeling the trajectory of a projectile or analyzing the shape of a curve, recognizing the significance of a vertex on the x-axis enhances the interpretation and utility of parabolic functions in diverse scenarios.