The function h(x) = x2 + 4x − 11 represents a parabola.

part a: rewrite the function in vertex form by completing the square. show your work.

part b: determine the vertex and indicate whether it is a maximum or a minimum on the graph. how do you know?

part c: determine the axis of symmetry for h(x).

Part A -

Part B - (h,k)=(-2,-15) , The minimum of the graph is at (-2,-15)

Part C - Axis of symmetry is x=-2

Step-by-step explanation:

Given : The function   represents a parabola.

Part A -

To find : Rewrite the function in vertex form by completing the square. Show your work.  

Solution :

The function

Vertex form is

We apply completing the square in given function,

The required vertex form is

Part B -

To find : Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?

Solution :

The vertex form is

where, (h,k) are the vertex of the function

On comparing with  

Vertex are (h,k)=(-2,-15)

For minimum or maximum we have to find the point

From given function a=1 and b=4

So,

The minimum value is at x=-2

Substitute in function we get, y=-15

Therefore, The minimum of the graph is at (-2,-15)

Part C -

To find : Determine the axis of symmetry for h(x).

Solution :

Axis of the symmetry is the x-coordinate of the vertex.

So, Axis of symmetry is x=-2