What is the axis of symmetry and vertex for the graph #y = 6x^2 + 24x + 16#?

1 Answer
Jun 14, 2017

The vertex is (-2,40) and the axis of symmetry is at x = -2.

Explanation:

  1. Complete the square to get the equation in the form #y = 4p(x-h)^2 +k#.
    y = 6(#x^2#+4x +4 ) + 16 +6(4)
    y = 6#(x+2)^2#+40
  2. From this equation, you can find the vertex to be (h,k), which is (-2,40). [Remember that #h# is negative in the original form, which means that the 2 next to the x becomes NEGATIVE.]
  3. This parabola opens upwards (because x is squared and positive), the axis of symmetry is x = something.
  4. The "something" comes from the x-value in the vertex because the axis of symmetry passes vertically through the middle of the parabola and the vertex.
  5. Looking at the vertex (-2,8), the x-value of the vertex is -2. Therefore, the axis of symmetry is at x = -2.