Question

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)

Answer 1

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

Answer 2

Answer:

Part A: The vertex form is h(x) = (x+7)^2  - 8 .

Part B: The vertex is a minimum. The vertex is (-7,-8).  

Part C: The axis of symmetry is x=-7. (axis of symmetry is the x value of the vertex)

Step-by-step explanation:

This video will help you understand how I got the function into vertex form.

Search: How do you convert from standard form to vertex form of a quadratic Brian McLogan

This will help you find the vertex

Search: Finding the vertex of a parabola in standard form khan academy