Question

Please help. I need help with a couple of questions. I will give medal and fan.

Answer 1

A toy rocket was launched from the ground. The function f(x) = -16x^2 + 192x shows the height of the rocket f(x), in feet, from the ground at time x seconds.

What is the axis of symmetry of the graph of f(x), and what does it represent?

x = 12; it takes 12 seconds to reach the maximum height and 12 seconds to fall back to the ground
x = 12; it takes 12 seconds to reach the maximum height and 24 seconds to fall back to the ground
x = 6; it takes 6 seconds to reach the maximum height and 6 seconds to fall back to the ground
x = 6; it takes 6 seconds to reach the maximum height and 3 seconds to fall back to the ground

Answer 2

I think its either C or D

Answer 3

i think it is not a 100% sure though

Answer 4

can you help me with a couple more?

Answer 5

yeah i will try

Answer 6

Functions f(x) and g(x) are shown below:

f(x) = x2
g(x) = x2 + 10x + 25

In which direction and by how many units should f(x) be shifted to obtain g(x)?

Right by 5 units
Left by 5 units
Right by 10 units
Left by 10 units

Answer 7

hint: (x^2 + 10x + 25) = (x+5)^2

Answer 8

so would it be D?

Answer 9

nope, please look carefully at what I wrote

(x+k)^2 moves the graph x^2 to the left k units

Answer 10

OK, B?

Answer 11

yes, B is the answer, but do you understand how to get (x+5)^2?

Answer 12

can you explain it a little, I sort of forgot.

Answer 13

have you seen this formula?

(a+b)^2 = a^2 + 2ab + b^2?

Answer 14

yes

Answer 15

great! in the equation x^2 + 10x + 25, do you see how x = a and b = 5? when you plug in x for a and b for 5, do you see how x^2 + 10x + 25 = (x+5)^2?

this is called "factoring", basically you want to find a and b so you can simplify x^2 + 10x + 25 into (x+5)^2

Answer 16

oh, I remember thanks!

Answer 17

do you mind helping me with a couple more?

Answer 18

sure, I guess

Answer 19

The steps to derive the quadratic formula are shown below:

Which of the following statements best describes the first incorrect step?

In Step 4, square of quantity of b over 2 times a instead of b over 2 times a was added on both sides.
In Step 5, x plus b over 2 times a, all squared was written instead of x plus b over 4a, all square.
In Step 6, c over a was written instead of -c over a inside the root.
In Step 7, square of quantity of b over 2 times a was written instead of b over 2 times a inside the root.

Answer 20

http://www.purplemath.com/modules/sqrquad2.htm

Answer 21

NOTE: I got this from a website, I didn't write this out myself, but these are the steps to derive the quadratic equation

Answer 22

David kicks a soccer ball off the ground and in the air, with an initial velocity of 35 feet per second. Using the formula H(t) = -16t2 + vt + s, what is the maximum height the soccer ball reaches?

Answer 23

for this one I know you plug in the 35 for v but what do you plug in for s?

Answer 24

v = initial velocity = 35, s = initial height = 0

Answer 25

an object on the ground has a height of 0

Answer 26

initial height = 0, because the ball is on the ground

Answer 27

ok I can do this one by myself

Answer 28

k cool

Answer 29

can you help me with 3 more?

Answer 30

ok

Answer 31

Water coming out from a fountain is modeled by the function f(x) = -x2 + 7x + 5 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 4 to x = 6 represent?

The water falls down with an average speed of 5 feet per second from 4 seconds to 6 seconds.
The water falls down with an average speed of 3 feet per second from 4 seconds to 6 seconds.
The water travels an average distance of 5 feet from 4 seconds to 6 seconds.
The water travels an average distance of 3 feet from 4 seconds to 6 seconds.

Answer 32

If 5p = -100 + 3Q2, which of the following could Q possibly be?

Q = square root of 5p-100/ 3
Q = square root of 5p+100/3
Q = square root of -5p+100/ 3
Q = square root of -5p-100/ 3

Answer 33

this one is a bit tough to explain but I'll try

average rate of change = speed = distance/time

the average rate of change between x = 6 seconds and x = 4 seconds =
distance travelled between 4 to 6 seconds/(6-4 seconds)

= [f(6)-f(4)]/(6-4)

Answer 34

and for the second one:

5p = -100 + 3Q^2

all you're doing is solving for Q in terms of p

add 100 to each side
divide each side by 3
take the square root of each side to find Q

Answer 35

35p=q^2
I got 5.9160797830996160425673282915616 when I did the square root of 35

Answer 36

??? I think you're confused, can I try outlining it step by step?

Answer 37

sorry I got confused I understand now.