The function p(x) = 6x2 + 48x written in vertex form is p(x) = 6(x + 4)2 – 96. which statements are true about the graph of p? check all that apply.
a) the axis of symmetry is the line x = –4.
b) the graph is narrower than the graph of f(x) = x2.
c) the parabola has a maximum.
d) the parabola opens down.
e) the value of k is –96, so there is a vertical shift down 96 units.

The correct options are A, B and E.

Step-by-step explanation:

The given function is

Vertex form of the function is

                      ..... (1)

The vertex form of a parabola is

                          ..... (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 and if |a|<1, then graph is wider than the graph .

From (1) and (2), it is clear that

So we conclude that

1. The axis of symmetry is the line x = –4.

2. The graph is narrower than the graph of .

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.

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get,   becomes

2. the function is translated 5 units to the right.

so, we get,   becomes

3. the function is translated 5 units upwards.

so, we get,   becomes

4. the function is translated 5 units downwards.

so, we get,   becomes

5. the function is reflected across x-axis.

so, we get,   becomes

6. the function is reflected across y-axis.

so, we get,   becomes .

step-by-step explanation:

mark brainliest.