Answer:
The correct options are A, B and E.
Step-by-step explanation:
The given function is
[tex]p(x)=6x^2+48x[/tex]
Vertex form of the function is
[tex]p(x)=6(x+4)^2-96[/tex] ..... (1)
The vertex form of a parabola is
[tex]f(x)=a(x-h)^2+k[/tex] ..... (2)
where, (h,k) is vertex and x=h is the axis of symmetry.
If a>0, then parabola opens up and if a<0, then parabola opens down.
If |a|>1, then graph is narrower than the graph of [tex]f(x)=x^2[/tex] and if |a|<1, then graph is wider than the graph [tex]f(x)=x^2[/tex] .
From (1) and (2), it is clear that
[tex]a=6, h=-4, k=-96[/tex]
So we conclude that
1. The axis of symmetry is the line x = –4.
2. The graph is narrower than the graph of [tex]f(x)=x^2[/tex].
3. The parabola has a minimum.
4. The parabola opens up.
5. The value of k is –96, so there is a vertical shift down 96 units.
Therefore options A, B and E are correct.
