Answer:
The equation that represents the equation of the parabola is:
[tex]y=4(x+3)^2+2[/tex]
Step-by-step explanation:
We know that the general equation of the parabola with vertex at (h,k) is represented with the help of the equation:
[tex]y=a(x-h)^2+k[/tex]
where a is a constant and if a>0 then the parabola is open upward.
and if a<0 then the parabola is open downward.
Here we have the vertex of the parabola at (-3,2)
and a=4 in each of the options.
i.e. we have: h=-3 and k=2
Hence, the equation of the parabola is:
[tex]y=4(x-(-3))^2+2\\\\i.e.\\\\y=4(x+3)^2+2[/tex]
The correct option is:
Option: B
