Question

PLEASE HELP?

A ball is launched from a slingshot. Its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.

After 1 second, the ball is 148 feet in the air, after 2 seconds the ball is 272 feet in the air.

Find the height in feet of the ball after 6 seconds in the air?

Answer 1

A quadratic equation has the form\[Ax^2+Bx+C=h(x)\]is there anything in the problem that indicates the initial height of the ball before launch is zero?

Answer 2

I'm not sure how to use that form to get the answer. From reading the problem I do not see anything that indicates the initial height of the ball. Just what it is at after 1 second, and then after 2 seconds.

Answer 3

y is this q yellow

Answer 4

Qualified helper. He used OwlBucks

Answer 5

oh

Answer 6

Isn't it \(\sf H(t) = -16t^2 + vt + s\)?

Answer 7

I guess we can say that h(x) represents the change in height from its initial position. If we can do that we can say the equation is of the form\[Ax^2+Bx=h(x)\]we know that when x=1, h(x)=148, so we can get an equation from that.

Answer 8

I'm confused :/

Answer 9

when x=2, h(x)=272, so plugging that in gives another equation
we can then solve the system of equations to find A and B

Answer 10

@iGreen I think this question assumes no knowledge of physics

Answer 11

Oh, okay.

Answer 12

@paigeally are you expected to know the acceleration of gravity? Is it given anywhere?

Answer 13

No it doesn't expect physics, or gravity. It's just a quadratic function question where I have to find a function that'll work to find out what 6 seconds is. It's from Alegbra 2

Answer 14

Then I will say that h(x) represents the change in height, and so a quadratic formula that expresses this is\[h(x)=Ax^2+Bx\]When x=1, h(x)=148, so we can write\[h(1)=A(1)^2+B(1)^2=148\]

Answer 15

I searched for help for the same question, and a similar problem with different words and number came up, and it showed a way to figure it out but I couldn't understand it.

Answer 16

How can I use that formula you gave me to figure the answer?
I'm not sure what goes in A,B, or C

Answer 17

but do you understand what I said in my last post?
this gives us an equation with two unknowns (A and B)

Answer 18

We have to assume C=0, or else the problem cannot be solved. For that reason I don't like the wording of the question.

Answer 19

I think that the height can be modeled by the subsequent function:
\[\Large h\left( x \right) = a{x^2} + b\]

Answer 20

Can I post the similar solution to a similar question, and maybe that will help you explain what I need to do?

Answer 21

sure

Answer 22

A ball is launched from a sling shot. After 1 second, the ball is 121 feet in the air. After 2 seconds, it's 224 feet in the air. Using quadratic functions, find the height, in feet, of the ball after 3 seconds in the air.

0a +0b +c = 0 ; c = 0
----------------------------

a + b = 121 ; a = 121-b
-----------------------------

4a +2b = 224
4(121-b) + 2b = 224
484 -4b +2b = 224
484 - 224 = 2b
260/2 = b ; b = 130
------------------------------

a + 130 = 121
a = 121 - 130 ; a = -9
------------------------------------

our quadratic formula becomes:

y = -9x^2 +130x

y = -9(3)^2+130(3)
y = -81 + 390

y = 309 ; the height is 309 ft after 3 seconds.

Answer 23

ok good, that is the method I am doing

Answer 24

they also assumed c=0
so again, we have the formula\[Ax^2+Bx=h(x)\]we know that when x=1, h(x)=148 (in other words, h(1)=148)
so plug those numbers into this equation and you get \[A(1)^2+B(1)=148\]which simplifies to \[A+B=148\]so far so good?

Answer 25

Yes so far I follow

Answer 26

ok, now we also know that h(2)=272, so again we can plug x=2 into our equation, and we get\[A(2)^2+B(2)=272\]which simplifies to what?

Answer 27

A+b=272 ?

Answer 28

\(A*2^2=4A\)

Answer 29

\(B*2=2B\)

Answer 30

Alright I see how you got that

Answer 31

good, so we have two equations:\[A+B=148\\4A+2B=272\]this is a system of two equations with two unknowns, which means it can be solved. Do you know how to do this using substitution?

Answer 32

No, I don't. Math isn't my forte.

Answer 33

well, we want to get it so one of the equations has only one variable in it. An easy way to do that in this case is to solve for either A or B in the first equation, then substitute that into the second equation.
Can you solve the first equation for B?

Answer 34

It could be any number though, how do I know what the right one is?

Answer 35

I mean solve \(A+B=148\) for B. In other words, get it into the form where B is alone on one side and A and 148 are on the other, i.e.\[B=...\]

Answer 36

I'm not following, do you mean pick two numbers to fill in for A and B?

Answer 37

no, I mean subtract A from both sides