Answer :
Answer:
Options 4, 5 and 7.
Step-by-step explanation:
The general function is
[tex]f(x)=x^2[/tex]
The vertex form of a parabola,
[tex]g(x)=a(x-h)^2+k[/tex] ...(1)
where, a is a constant and (h,k) is vertex.
It is given that vertex of a parabola is (-1,-2).
[tex]g(x)=a(x-(-1))^2+(-2)[/tex]
[tex]g(x)=a(x+1)^2-2[/tex] ...(2)
It passes through (-3,-3).
[tex]-3=a(-3+1)^2-2[/tex]
[tex]-3+2=4a[/tex]
[tex]-1=4a[/tex]
[tex]-\dfrac{1}{4}=a[/tex]
Put this value in (2).
[tex]g(x)=-\dfrac{1}{4}(x+1)^2-2[/tex]
Now,
h=1>0, so translation of 1 unit left.
a=-1/4<0 Reflection across the x-axis and vertical compression by factor 4.
k=-2<0, translation of 2 units down
Therefore, the correct options are 4, 5 and 7.