Question

The functions f(x) = −(x + 4)2 + 2 and g(x) = (x − 2)2 − 2 have been rewritten using the completing-the-square method. Apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.

Answer 1

We can consider an expression like x^2. The shape of the graph of this expression is an upward-facing parabola. The vertex lies at the bottom of this parabola, so it is a minimum. On the other hand, and expression like -x^2 would produce a downward facing parabola. So, the vertex of that graph would be a maximum.
Based on the positive and negative signs of the functions above, I think you can tell which one has a vertex that is a maximum and which has a vertex that is a minimum

Answer 2

Ok so first if a > 0 then the parabola shall open upwards and the vertex will be the minimum point. 

And if a < 0 then the parabola shall open downwards and the vertex will be the maximum point.

So with saying that for f(x) a = -1, the vertex is (-4,2). Therefore, a < 0 the parabola will open downward, and the vertex shall be the maximum point.

And g(x) a = 1, the vertex is (2,-2). Therefore, a > 0 the parabola will open upward, and the vertex shall be the minimum point.