Question

A toy rocket was launched from the ground. The function f(x) = -6x^2 + 256x shows the height of the rocket f(x), in feet, from the found at time x seconds. What is the axis of symmetry of the graph of f(x), and what does it represent?
~ x=8; it takes 8 sec. to reach the max. height and 8 sec. to fall back to the ground.
~ x=16; it takes 16 sec. to reach the max. height and 16 sec. to fall back to the ground.
~ x=8; it takes 8 sec. to reach the max. height and 16 sec. to fall back to the ground.
~ x=16; it takes 16 sec. to reach the max. height and 32 sec. to fall back to the ground.

Answer 1

I think it's A, but I'm not sure.

Answer 2

add them with all of the numbers and do one at a time

Answer 3

I have no idea what that means. What am I supposed to add?

Answer 4

If I solve that then answer is 16,000.

Answer 5

@mathmale Do you think you can help me please?

Answer 6

The function f(x) = -6x^2 + 256x shows the height of the rocket f(x), in feet, from the found at time x seconds. What is the axis of symmetry of the graph of f(x), and what does it represent?

This is a quadratic function of the form y=ax^2 + bx + c.

the equation of the axis of symmetry is \[x=\frac{ -b }{ 2a }\]Please obtain a and b from the given equation for f(x), substitute them into the above formula, and write the result as an equation. That equation represents your axis of symmetry.

Answer 7

@HMT? As tempting as it may be to look around while waiting for someone to answer your question, it'd be more polite and more effective to stay with your own question, don't you think?

Answer 8

Unfortunately, I now need to get off the Internet.

Answer 9

The problem can be answered by a different way.
There is nothing related to the parabola graph and vertex.
When the rocket reach the max height, its begins to fall down by the equation -gt^2/2= -4.9*t^2 , with initial velocity zero. The falling down takes more time than the rising time. I would choose Answer c: rising time 8 sec and falling time 16 sec.

Answer 10

Reason to choose answer c.
After 8 sec, the max height is : y = (-6)(64) + 256(8) = 1536 - 384 = 1,152 ft
Time for the falling down, from the same height (1,152)
(4.8)*t^2 = 1,152 -> t^2 = 1152/4.81= 240 --> t # 16 sec.

Answer 11

Ooh, ok. I was going to ask you why it would take longer to fall down. Thank you :)

Answer 12

Time for falling down with the same distance 1,152 ft is given by the equation:
y = gt^2/2 + vo*t, with initial velocity Vo = 0.
1,152 = 4.9 *t^2 --> t^2 = 1152/4.9 = 235. --> t = 15.33 # 16 sec

Answer 13

Ok, thank you for your help!