Vertex and the maximum or minimum value

Question

Without graphing, find the vertex and the maximum or minimum value of f(x).
f(x)=5(x-8)²+4
What is the vertex?

(Type an ordered pair.)
Is there a maximum or minimum value of f(x)?


What is the minimum value of f(x)?

Answer 1

The main trick to this problem is knowing this rule:

y=a(x-h)²+k

Where the vertex is (h,k).

That would mean the vertex, in this case, is (8,4) because h=8 and k=4.

The formula, y=a(x-h)²+k, is that it is the graph of a quadratic equation that is "concave up" (like a letter 'u'). This means it can only have a minimum, which, in this case is your vertex.