Answer:
The vertex form of the given equation is [tex]y=-3(x+2)^2+10[/tex].
Step-by-step explanation:
The vertex form of a parabola is
[tex]y=a(x-h)^2+k[/tex].
The given equation is
[tex]y=-3x^2-12x-2[/tex]
[tex]y=(-3x^2-12x)-2[/tex]
Take the common coefficients.
[tex]y=-3(x^2+4x)-2[/tex]
If an expression is defined as [tex]x^2+bx[/tex], then we need to add [tex](\frac{b}{2})^2[/tex] to make it perfect square.
Here b=4, so we need to add [tex](\frac{4}{2})^2[/tex] in the parenthesis.
[tex]y=-3(x^2+4x+2^2-2^2)-2[/tex]
[tex]y=-3(x^2+4x+2^2)-3(-2^2)-2[/tex]
[tex]y=-3(x+2)^2-3(-4)-2[/tex]
[tex]y=-3(x+2)^2+12-2[/tex]
[tex]y=-3(x+2)^2+10[/tex]
Therefore the vertex form of the given equation is [tex]y=-3(x+2)^2+10[/tex].
