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.

50.6

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~