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:
- 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 - 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.] - This parabola opens upwards (because x is squared and positive), the axis of symmetry is x = something.
- 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.
- Looking at the vertex (-2,8), the x-value of the vertex is -2. Therefore, the axis of symmetry is at x = -2.