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

if this is really you s much. i only have 3 points left and i have 2 questions to ask

answer is d-29

step-by-step explanation:

since you didn't include the picture, i can give you the description so you know how to pick the correct answer. the third quartile of a data is always shown in a box plot. in the middle of your graph should be a box. the third quartile is the value that goes with the far right edge of the box.