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. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.

Answer 1

The vertex form of a quadratic function: $y=a(x-h)^2+k$.
If a>0, then the parabola opens upwards and the vertex is the minimum of the function.
If a<0, then the parabola opens downwards and the vertex is the maximum of the function.

$f(x)=-(x+4)^2+2 \\ \Downarrow \\ a=-1$
a<0, so the vertex is the maximum of the function.

$g(x)=(x-2)^2-2 \\ \Downarrow \\ a=1$
a>0, so the vertex is the minimum of the function.