The functions f(x) = -(x-1)^2 + 5 and g(x) = (x+2)^2 - 3 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.

a) f(x) has a maximum vertex

b) g(x) has a minimum vertex

Step-by-step explanation:

The function

has its vertex at (h,k).

If a>0, then (h,k) is a minimum vertex.

If a<0, then (h,k) is a maximum vertex.

The first function is

a=-1<0, therefore the vertex (1,5) is the maximum point.

The second function is

a=1>0, therefore the vertex (-2,-3) is a minimum point.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.