If \( a>0 \) and \( f(x)=a(x-h)^{2}+k \), then \( k \) is the ___ value of the function.

If \( a>0 \) and \( f(x)=a(x-h)^{2}+k \), then \( k \) is the minimum value of the function. This is because the graph of a quadratic function opens upwards when the coefficient \( a \) is positive, which means that the vertex (\( h, k \)) represents the lowest point on the graph. The vertex form of a quadratic function is not just useful for identifying the minimum (or maximum) value; it also allows you to quickly sketch the graph. By knowing the vertex \( (h, k) \), you can easily plot the turning point and determine the direction the parabola opens, providing a beautiful picture of how the function behaves!