Question

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

Answer 1

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.