Question

Plot on graph.

Answer 1

Answer:

Axis of symmetry: x=-2

Maximum point: (-2,8)

Step-by-step explanation:

The given function is $h(x)=-\frac{1}{2}x^2-2x+6$.

We can complete the square to reveal the axis of symmetry and the vertex.

We factor to get:

$h(x)=-\frac{1}{2}(x^2+4x)+6$

We add the zero pairs and obtain a perfect square:

$h(x)=-\frac{1}{2}(x^2+4x+4-4)+6$

$h(x)=-\frac{1}{2}(x^2+4x+4)+2+6$

$h(x)=-\frac{1}{2}(x+2)^2+8$

The function is now in the form $h(x)=a(x-h)^2+k$, where V(h,k) =(-2,8) is the vertex.