If \( a>0 \), the graph of \( f(x)=a(x-h)^{2}+k \) opens

The graph of \( f(x) = a(x-h)^2 + k \) opens upwards because \( a > 0 \). This is characteristic of a quadratic function in vertex form, where the vertex is at the point \( (h, k) \). When \( a \) is positive, the parabola's arms extend upwards, creating a shape that indicates the function has a minimum point at the vertex. Additionally, the values of \( h \) and \( k \) determine the position of the vertex on the Cartesian plane, making this form especially useful for graphing. It allows for an easy identification of the vertex's coordinates and gives insights into the function’s behavior around that point!