Question

PLEASE HELP!!! write a quadratic function, h(t), that shows the height, in feet, of the soccer ball, t seconds after it was kicked. Use the general equationh(t)= - 16t^{2} + v_{0}t + h_{0} where v_o is the initial velocity and h_o is the initial height. Show how you got the x-intercepts, the vertex's as well as graph it. How long was the soccer ball in the air?

Answer 1

I dont get it, can you make up your equation_

Answer 2

Idk, it doesn't give me another equation for it

Answer 3

is there a picture?

Answer 4

I'll give you one

Answer 5

a picture is needed for this i guess,

Answer 6

like associated with the problem is what i meant

Answer 7

This isn't the full of it but here you go

Answer 8

I gtg, sorry. Ask someone else to help you. I will get back to you later maybe

Answer 9

ok, no problem

Answer 10

Can you send the rest of the question, by any chance?

Answer 11

yeah

Answer 12

here is one and I'll send the last bit right now

Answer 13

I wonder what is in the "show your work" part.

Answer 14

they are all blank

Answer 15

Says to click that first before writing the quadratic equation.

Answer 16

yeah, thats why there was no problem

Answer 17

then it says "of THE soccer ball" which implies they presented you with a problem scenario to begin with. I don't see where you have posted the initial problem statement.

Answer 18

i am so sorry there was fine print I was missing, I apologize for wasting your time, it had an initial velocity of 96 ft per second. I didn't see the fine print right above it

Answer 19

Can you just please screenshot the initial problem statement?

Answer 20

I don't know why you've posted everything else but avoided posting the initial problem statement when that is the most essential piece of this puzzle to post.

Answer 21

ok

Answer 22

Yes, now we know essential things like "The ball was kicked vertically while on the ground"

Answer 23

I'm sorry. I didn't see that part

Answer 24

Yes because we now know that \(h_0\), the initial height of the ball at \(t = 0\) is also zero since the ball is on the ground and not on a roof.

Answer 25

We also now know that \(v_0\) the initial velocity is 96 feet per second.

Answer 26

Knowing all this information, we are able to set up the quadratic function.

Answer 27

If \(v_0 = 96\) and \(h_0 = 0\) how do you suppose we might write the expression for \(h(t)\)?

Answer 28

plug in 96 for \[v_0\] and 0 for \[h_0\]

Answer 29

Correct and what would that look like if we did that? Can you write out the entire function?

Answer 30

that would look like h(t) = -16t2 + \[96t + 0\]

Answer 31

If we're using correct notation it would be \(h(t) = -16t^2 + 96t + 0\). If you're not familiar with LaTeX just put a caret between the t and the 2:
h(t) = -16t^2 + 96t + 0

Answer 32

oh, right
forgot about that

Answer 33

alright I got the equation plugged in and I assume I would treat it like a regular quadratic function and find a, b, and c, and then solve using that?

Answer 34

a, b and c is already given. You can determine that from the function

Answer 35

right but I mean solve using a b and c

Answer 36

The problem is asking you to write a function and you have already done that. So you are done

Answer 37

Or did you need anything else?

Answer 38

there is more, I have to find x intercepts, vertex, then graph, and then find how long the ball was in the air

Answer 39

oh okay. To find the x-intercepts you can use the quadratic formula

Answer 40

remember to find the x-coor of the vertex you can use the formula (-b/2a) and then plug that in for y

Answer 41

ok

Answer 42

and then ur basically done

Answer 43

graph it then find the time when the ball hits the ground, or the second x-intercept. Since we are talking about t then the time it takes for the ball to drop is how much time it was in the air because we started from 0

Answer 44

it says t=(6,0), would that be x intercept 1?

Answer 45

where does it say that?

Answer 46

oh you mean that the x-intercepts are at 6,0 and 0,0

Answer 47

good job

Answer 48

I'm using mathway for the quadratic formula since I don't got a lot of time

Answer 49

so how long was that ball in the air?

Answer 50

no im pretty sure it says that ur x-intercept is at 6

Answer 51

Now find the time it stayed in the air?

Answer 52

150 seconds?

Answer 53

why?

Answer 54

a visual might be easier to use to explain

Answer 55

hold on, ill graph this using desmos then show u

Answer 56

so as you can see here, the 2 x-intercepts

Answer 57

how much time does it take the ball to drop is the same as how long it is in the air
Can you figure it out?

Answer 58

oh, six seconds

Answer 59

dang, that is one high and steep kick

Answer 60

ye lol

Answer 61

u got it, keep it up :0

Answer 62

thanks

Answer 63

wait, can someone show me the steps to solving this with quadratic formula?

Answer 64

oh yeah sorry

Answer 65

so once you find the x-intercepts that is when the ball hits the ground right?

Answer 66

so the x-intercepts were 6 and 0 and it takes 6 seconds to drop

Answer 67

plug in the numbers