Question

What is the axis of symmetry and vertex for the graph `y=x^2+8x+12`?

Answer 1

The axis of symmetry is `x = -4`, the vertex is `(4, -4)`

Explanation:

We can find the axis of symmetry in the form of a line, `x`

To find the value of line `x`, we use this equation:
`x = (-b)/(2a)`.

In our given graph, `a = 1`, and `b = 8`

After inserting values:

`x = (-8)/(2*1) = (-8)/2 = -4`

The equation for our axis of symmetry is `x = -4`

To find the vertex, we must convert our parabola's equation to vertex form: `y = a(x - h)^2 + k`. We can do this by completing the square.

`y = x^2 + 8x + 12`

`y - 12 = x^2 + 8x`

`y - 12 + 16= x^2 + 8x + 16`

`y + 4= (x + 4)^2`

`y = (x+4)^2 - 4`

`h = -4, k = -4`

Our vertex is h,k, and thus, (-4,-4).