The function h(x) = x2 + 14x + 41 represents a parabola. part a: rewrite the function in vertex form by completing the square. show your work. (6 points) part b: determine the vertex and indicate whether it is a maximum or a minimum on the graph. how do you know? (2 points) part c: determine the axis of symmetry for h(x). (2 points)

Part A:



The first thing of completing the square is writing the expression   as   which expands to  .

We have the first two terms exactly alike with the function we start with:  and   but we need to add/subtract from the last term, 49, to obtain 41. 

So, the second step is to subtract -8 from the expression 

The function in finalizing the square form is


Part B:

The vertex is acquired by equating the expression in the bracket from part A to zero




It means the curve has a turning point at x = -7

This vertex is a minimum since the function will make a U-shape. 
A quadratic function   can either make U-shape or ∩-shape depends on the value of the constant   that goes with  . When   is (+), the curve is U-shape. When   (-), the curve is ∩-shape

Part C:

The symmetry line of the curve will go through the vertex, hence the symmetry line is 

This function is shown in the diagram below

d 192

step-by-step explanation:

we find our area to find area we multiply thoses numbers to get our answer so our area is 192

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )