Answer:
The vertex form of the given equation is
.
Step-by-step explanation:
The vertex form of a parabola is
.
The given equation is
![y=-3x^2-12x-2](https://tex.z-dn.net/?f=y%3D-3x%5E2-12x-2)
![y=(-3x^2-12x)-2](https://tex.z-dn.net/?f=y%3D%28-3x%5E2-12x%29-2)
Take the common coefficients.
![y=-3(x^2+4x)-2](https://tex.z-dn.net/?f=y%3D-3%28x%5E2%2B4x%29-2)
If an expression is defined as
, then we need to add
to make it perfect square.
Here b=4, so we need to add
in the parenthesis.
![y=-3(x^2+4x+2^2-2^2)-2](https://tex.z-dn.net/?f=y%3D-3%28x%5E2%2B4x%2B2%5E2-2%5E2%29-2)
![y=-3(x^2+4x+2^2)-3(-2^2)-2](https://tex.z-dn.net/?f=y%3D-3%28x%5E2%2B4x%2B2%5E2%29-3%28-2%5E2%29-2)
![y=-3(x+2)^2-3(-4)-2](https://tex.z-dn.net/?f=y%3D-3%28x%2B2%29%5E2-3%28-4%29-2)
![y=-3(x+2)^2+12-2](https://tex.z-dn.net/?f=y%3D-3%28x%2B2%29%5E2%2B12-2)
![y=-3(x+2)^2+10](https://tex.z-dn.net/?f=y%3D-3%28x%2B2%29%5E2%2B10)
Therefore the vertex form of the given equation is
.