Question

Can someone PLEASE help me? Will fan/give medal
A Labrador leaps over a hurdle. The function f(t) represents the height of the Labrador above the ground, in inches, at t seconds:

f(t) = -16t2 + 26t

A foxhound jumps over the same hurdle. The table shows the height of the foxhound above the ground g(t), in inches, at t seconds:

Time (t) g(t)
0 0
0.4 6.24
0.6 7.44
0.7 7.56
0.8 7.36
1.0 6
1.4 0

Answer 1

Part A: Compare and interpret the maximum of f(t) and g(t)? (4 points)

Part B: Which function has a greater x-intercept? What do the x-intercepts of the graphs of f(t) and g(t) represent? (4 points)

Part C: Determine the y-intercepts of both functions, and explain what this means in the context of the problem. (2 points)

Answer 2

https://answers.yahoo.com/question/index?qid=20140414130742AAFPTrv
this might help

I took algebra last year early in the year
I don't remember how to do most of this but I took it for sure

Answer 3

Notice since our quadratic has a \(-a\) term, it opens down and therfore has a maximum halfway between the two zeros. Solving for the zeros we get:
\[-16t^2 +26 t = 0\\ 2t(-8t+13)=0 \\2t = 0 \text{ and } -8t+13 = 0\\ t_1= 0 \text{ and } t_2 = \frac{13}{8} \]

Finding the halfway point between \( 0 \) and \(\frac{13}{8}\) gives us \(t_{max} = \frac{13}{16} \). So the max output is:
\[f(t_{max}) = -16 \left (\frac{13}{16}\right)^2 + 26 \frac{13}{16} = \frac{169}{16} \]

Answer 4

I thought I had to find the maximum and it would be 13/16 for x?

Answer 5

Woahhh I think im confusing myself

Answer 6

By my calculations the maximum is 13/16

Answer 7

t is time, and t=13/16 seconds when the function is maximum, have to plug that in to find the maximum height.

Answer 8

the maximum occurs at \(t = \frac{13}{16} \), but this is not what the function max

Answer 9

Ok....So then it would be 169/16?

Answer 10

Correct, now you can compare to \(g(t)\)

Answer 11

So 169/16 which is in decimal form 10.5625 would beat the 0.7 and 7.54?

Answer 12

0.7 and 7.54 for the foxhound

Answer 13

Correct, that max of f is greater than the max of g, what does this mean physically (in terms of the problem)?

Answer 14

The lab jumps higher?

Answer 15

Precisely, so for part b it is askign which one has a greater x-int. Remember x-intercepts occur when \(f(x) = 0\) (or) \(g(x) = 0\). If we can find these, we can compare. I believe g is clear, and the f has already been calculated once in here.


What does the x-intercept mean physically?

Answer 16

small typo, x =t here.

Answer 17

The labs x-intercept is (0,0),(138,0)?

Answer 18

so does that mean either are greater for the intercept?

Answer 19

neither *

Answer 20

excuse me
You are correct

Answer 21

Yes, so 13/8 was the greatest x int of f(t) which doesn't beat out g(t). What does this tell us physically?

Answer 22

I'm not sure

Answer 23

Ah, so this is measuring the height the dogs jump. That is \(f(t), g(t) \) tells us how high they have reached at some time, t. So if they are both zero, the dogs are where (spatially?)

Answer 24

they're jumping the same height?

Answer 25

or one isnt jumping any higher than the other?

Answer 26

Well this equation models one jump for each dog. So when you jump you reach a maximum and then you start to fall, eventually you reach the floor. This is when your x-intercept occurs. So which dog hit the ground first?

Answer 27

The foxhound?

Answer 28

I'm not sure how much the foxhound jumped because I dont really understand how to map out that kind of table

Answer 29

Correct, the x-intercepts for the fox hound are \((0, 0) and (1.4, 0\)). So at t = 1.4, the foxhound hit the floor. The lab hit the floor at t = 1.62. Physically this max sense since the lab jumped higher than the foxhound.

Answer 30

Note 1.62 = 13/8

Answer 31

Oh wow! and thats it for the problem??

Answer 32

I have to head out, so finally part c wants to look for the y -ints. This occurs when \(t = 0\). The only y intercepts are \((0,0)\) for both dogs. Physically, this means at time zero they were on the floor since \(f(t), g(t) =0\). This isn't always the case, it is possible for one dog to jump from the ground while the other jumps from a ledge.

Answer 33

So they would both have the y-intc as (0,0)?

Answer 34

Yes, meaning they both started at ground level at the beginning of the jump.

Answer 35

Ok, thank you so much!

Answer 36

You're welcome. I hope it cleared things up.

Answer 37

I really appreciate it!