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

1 Answer
May 10, 2018

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).