How do you find the axis of symmetry and vertex point of the function: #y=x^2+12x-9#?

1 Answer
Oct 8, 2015

Axis of Symmetry: #x=-6#
Vertex: #(-6,-45)#

Explanation:

The first thing you must do, is convert this equation to vertex form #y=a(x-h)^2+k#. Finding the axis of symmetry and the vertex will become easy after that.

Converting to Vertex Form (#y=a(x-h)^2+k#)
#y=x^2+12x-9#
#y+9=x^2+12x#
#y+9+36=x^2+12x+36#
#y+45=(x+6)^2#
#color(red)(y=(x+6)^2-45)#

Axis of Symmetry
The axis of symmetry is #x=h#. Just by looking at the equation in vertex form, you will see that #h=-6#.

Therefore, the axis of symmetry is:

#x=h#
#color(blue)(x=-6)#

Vertex
The vertex is #(h,k)#. Again, just look at the equation and you will see that #h=-6# and #k=-45#.

Therefore, the vertex is:

#(h,k)#
#color(magenta)((-6,-45)#