Question

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.

Answer 1

a,b,e is the answer to this question

Answer 2

The correct options are A, B and E.

Explanation:

The given function is

`p(x)=6x^2+48x`

Vertex form of the function is

`p(x)=6(x+4)^2-96` ..... (1)

The vertex form of a parabola is

`f(x)=a(x-h)^2+k` ..... (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
`f(x)=x^2` and if |a|<1, then graph is wider than the graph
`f(x)=x^2` .

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

`a=6, h=-4, k=-96`

So we conclude that

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

2. The graph is narrower than the graph of
`f(x)=x^2`.

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.