Equation of the parabola is represented by the following expression (vertex form):
[tex]y=a(x-h)+k[/tex]
In this equation, the vertex of the parabola is the point (h, k)
Then, in this case the vertex of the parabola would be:
[tex]\begin{gathered} f(x)=(x-3)^2+14 \\ \text{Vertex: (3, 14)} \end{gathered}[/tex]
If the coefficient of the square x term is negative, the vertex will be the highest point on the graph, but if the coefficient of the square x term is positive, the vertex will be the lowest point on the graph.
Vertex: (3, 14) is an absolute minimum because the coefficient of the square x term is +1.
