Question

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 + 20t

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 7.04
0.6 8.64
0.75 9
1.0 8
1.5 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

@One098

Answer 3

i need help

Answer 4

http://openstudy.com/study#/updates/53472cb6e4b01730eeaf79fd

Answer 5

not really but thanx anyway

Answer 6

@ganeshie8

Answer 7

can you help me please

Answer 8

which part ?

Answer 9

all of them

Answer 10

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

Answer 11

Look at the table of foxhound,
whats its max height ?

Answer 12

8.64

Answer 13

Time (t) g(t)
0 0
0.4 7.04
0.6 8.64
0.75 `9`
1.0 8
1.5 0

Answer 14

did you miss 9 ?

Answer 15

yeah

Answer 16

so the maximum height reached by foxhound/g(t) is `9`

Answer 17

what about Labrador/f(t) ?

Answer 18

\(\large f(t) = -16t^2 + 20t\)

Answer 19

when i graph it it say 6.25

Answer 20

do you know how to find the maximum height of this parabola ?

Answer 21

You're right! so the labrador/f(t) reaches only a max height of 6.25

Answer 22

not really im not good at parabola

Answer 23

but i guess im good at graphing

Answer 24

thats very good :) so are we done with part a

Answer 25

ok can you help me with part b

Answer 26

how would i find the x-intercepts on this?

Answer 27

if you want to find the max height reached by labrador/f(t) algenraically :

\(\large f(t) = -16t^2 + 20t\)

\(\large -b/2a = -20/-2*16 = 5/8\)
max height = \(\large f(5/8) = -16(5/8)^2 + 20(5/8) = 25/4 = 6.25\)

Answer 28

that was still for part a ^^

Answer 29

ok that makes sense

Answer 30

So clearly the foxhound reached greatest height.. thats the interpretation ok

Answer 31

lets see part b

Answer 32

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)

Answer 33

x-intercept occurs when the function becomes 0

Answer 34

Time (t) g(t)
`0 0`
0.4 7.04
0.6 8.64
0.75 9
1.0 8
`1.5 0 `

Answer 35

the x intercepts of foxhound/g(t) are 0, 1.5
they tell you that the foxhound has started leaping at t=0 and fell at t=1.5

Answer 36

so the foxhound is in air for 1.5 seconds.

is that clear ?

Answer 37

can you find the x intercepts for labrador/f(t) ?

\(\large f(t) = -16t^2 + 20t\)

Answer 38

sorry lag my internet

Answer 39

its okie

Answer 40

just set that expression equal to 0 and solve t

Answer 41

\( \large -16t^2 + 20t = 0\)

Answer 42

so would i replace t for 0 into f(t)

Answer 43

factor the GCF and solve t

Answer 44

not yet. we will be doing that for part c, for y intercepts.

Answer 45

for x intercepts, you need to solve above equation

Answer 46

the gcf is 4 correct

Answer 47

4t

Answer 48

or may be -4t

Answer 49

176

Answer 50

\(\large -16t^2 + 20t = 0 \)

\(\large -4t(4t -5) = 0 \)

\(\large t = 0\) or \(\large t = 5/4 = 1.25\)

Answer 51

so the labrador is in air for exactly 1.25 seconds

Answer 52

oh ok im sorry i got a little confused man im an idiot

Answer 53

no you're not

Answer 54

it seems foxhound is in air for longer time than the labrador ?

Answer 55

np :) can you finish part c on ur own ?

Answer 56

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

Answer 57

y intercept the value of function at t=0

Answer 58

Time (t) g(t)
`0 0`
0.4 7.04
0.6 8.64
0.75 9
1.0 8
1.5 0

Answer 59

actually i need help on that i jumped the gun a bit

Answer 60

for foxhound/g(t) the x intercept is 0,
that means the foxhound started from ground, from 0 height

Answer 61

oh ok and its the same thing for the Labrador correct

Answer 62

what about the y intercept of labrador/f(t) ?

Answer 63

yup! but u need to show why its the same

Answer 64

f(t)=-16(0)^2 + 20(0)

Answer 65

Perfect!

Answer 66

so they both have started from the ground at 0 height

Answer 67

Yay thank you so much you are the best

Answer 68

yw:)