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

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Answer 1 · 2017-06-14T02:02:31

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

Complete the square to get the equation in the form $y = 4 p {(x - h)}^{2} + k$ $y = 4p(x-h)^2 +k$ .
y = 6( $x^{2}$ $x^2$ +4x +4 ) + 16 +6(4)
y = 6 ${(x + 2)}^{2}$ $(x+2)^2$ +40
From this equation, you can find the vertex to be (h,k), which is (-2,40). [Remember that $h$ $h$ 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.

What is the axis of symmetry and vertex for the graph y=6x2+24x+16y = 6x^2 + 24x + 16?