Question

HELP with Quadratic Formula Word Problems!! One of the games at a carnival involves trying to ring a bell with a ball by h(t)= -16t + 39t. If the bell is 25 ft. above the ground, will it be hit by the bell?

Answer 1

you said that this is a quadratic formula problem.

Is one of the terms in the equation supposed to be a t^2 ("t squared") term? Right now, it looks like h(t) = -16t + 39t which is just h(t) = 23t... not quadratic.

Answer 2

I was about to say that @JakeV8

Answer 3

@JakeV8 Yeah it's most likely not quadratic. My teacher just titled the worksheet quadratic problems, I didn't know what to call this other than putting the problem

Answer 4

Whoops sorry. wrong equation. it's h(t)= -16^2 + 39t.

Answer 5

:)

Answer 6

@JakeV8 @breja

Answer 7

Maybe like this? h(t) = -16t^2 + 39t

Answer 8

oh okay wait one sec

Answer 9

^^ Yeah it's that equation :) @JakeV8 sorry for the confusion!

Answer 10

because the other wasn't quadratic lol

Answer 11

h(t) = -16t2 + 39t dive both sides by t h = 39 + -16t simlify h = 39 + -16t

Answer 12

@dellzasaur, I don't think that last post was quite correct... but sorry to disappear... my page froze up.

h(t) = -16t^2 + 39t
I'm pretty certain this means that the height of the ball is given by the function h(t).

So, the question is, is there some value of "t" where the ball's height h(t) is equal to the bell's height of 25 feet.

Answer 13

So, if the ball hits the bell, then the ball's height h(t) will be = 25.

In other words, the question wants you to use the quadratic formula on the following:
25 = -16t^2 + 39t
So you would start by putting the 25 on the same side as the rest...
0 = -16t^2 + 39t - 25

Now you can use quadratic formula:
a = -16
b = 39
c = 25

Answer 14

@JakeV8 The funtion is odd

Answer 15

the function is odd

Answer 16

how so?

Answer 17

It is a function that is a parabola pointing down. This describes the motion of a ball thrown upward... imagine a softball thrown up high... it goes up, peaks at some height, then falls back to the ground.

Answer 18

okay

Answer 19

I've done a problem like this before but..okay @JakeV8

Answer 20

@breja, Earlier, when you said to divide both sides by "h", you just misunderstood the way they wrote the function. It wasn't "h times t" when they wrote "h(t)"...

h(t) is a function, or a rule, that tells what the ball's height is given some time "t" since it was thrown.

Answer 21

yea it was a mistake i read it wrong @JakeV8

Answer 22

0 = -16t^2 + 39t - 25

quadratic formula: a = -16, b = 39, c = 25

Solutions to h(t) are:
\[\frac{ -b \pm \sqrt{b^{2} -4ac} }{ 2a } = \frac{ -39 \pm \sqrt{39^{2} - 4(-16)(25)} }{ 2(-16) }\]

Answer 23

simplify:
\[\frac{ -39 \pm \sqrt{1521 - 1600} }{ (-32) } = \frac{-39 \pm \sqrt{-79}}{-32}\]

Answer 24

ur so smart

Answer 25

Uh oh :)

That means the solutions "t" that make h(t) = 25 involve a square root of a negative number.... bad news!!! There are no real numbers that are the square root of a negative...

That means there are no real number solutions that will allow h(t) to be equal to 25.

And what that really means is that there are no real solutions where the ball's height is equal to the bell's height of 25 feet...

In other words, no, the ball doesn't hit the bell.

@dellzasaur -- finally finished this one :)
@breja -- thank you :)

Answer 26

@JakeV8 Thank you so much!!!! I got that too :)

Answer 27

I tried @dellzasaur