Question

Identify the coordinates of the vertex of Alx) = (x - 3)2 + 14, and identify whether it's an absolute minimum or absolute maximum.

Answer 1

Equation of the parabola is represented by the following expression (vertex form):

$y=a(x-h)+k$

In this equation, the vertex of the parabola is the point (h, k)

Then, in this case the vertex of the parabola would be:

$\begin{gathered} f(x)=(x-3)^2+14 \\ \text{Vertex: (3, 14)} \end{gathered}$

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.