Question

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

Answer 1

A.
 = (x + 2)^2 - 4 - 11
= (x + 2)^2 - 15

B.   vertex  is at ( -2, -15) which is a minimum because the coefficient of x^2 is positive.

C.   The axis of symmetry is a vertical line passing through the vertex It is 
x = -2.

Answer 2

Answer:

Part A - $h(x)=(x+2)^2-15$

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  $h(x)=x^2+4x-11$ represents a parabola.

Part A -

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

Solution :

The function $h(x)=x^2+4x-11$

Vertex form is $f(x)=a(x-h)^2+k$

We apply completing the square in given function,

$h(x)=(x^2 + 4x + 2^2)-11-2^2$

$h(x)=(x+2)^2-15$

The required vertex form is $h(x)=(x+2)^2-15$

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 $f(x)=a(x-h)^2+k$

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

On comparing with  $h(x)=(x+2)^2-15$

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

For minimum or maximum we have to find the point $x=-\frac{b}{2a}$

From given function a=1 and b=4

So, $x=-\frac{4}{2(1)}$

$x=-2$

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