Question

An 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 5.44
0.6 6.24
0.7 6.16
0.8 5.76
1.0 4
1.2 0


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)

Answer 1

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

Ionly need help with part C

Answer 2

ok, it's asking for the y-intercepts, so we set t = 0 and find f(t) and g(t)

when t = 0, what does f(t) = ?

Answer 3

I dont know, this part is confusing me!

Answer 4

t = 0

f(t) = -16t^2 + 26t = ?

Answer 5

f(t)=-16^2=26t?

Answer 6

replace "t" with "0" and find f(t)

Answer 7

I dont understand, im having a moment

Answer 8

let's break it down step by step

t = 0

-16t^2 = __

fill in the blank

Answer 9

0? OR

Answer 10

good, -16t^2 = 0

Answer 11

next step:

t = 0

26t = ?

Answer 12

0?

Answer 13

good.

so f(t) = 0 when t = 0

that means the y-intercept of f(t) is 0

Answer 14

now, are you ready to find the y-intercept of g(t)?

Answer 15

I think i get lost when you said f(t)= 0 when t = 0?

Answer 16

ok, we are given the function

f(t) = -16t2 + 26t

to find the y-intercept, we must find the value of f(t) when t = 0, is that clear?

Answer 17

so we replace the ts with zeros?

Answer 18

yes

Answer 19

so, when t = 0

f(t) = -16t^2 + 26t = -16(0^2) + 26(0) = 0, is that clear?

Answer 20

so f(t)-16(0)^2+26(0)?

Answer 21

right, and we calculate that out

f(t)=16(0)^2+26(0) = 0

Answer 22

so our y-intercept is 0, is that clear?

Answer 23

I dont understand

Answer 24

how do we find the y intercept

Answer 25

we just found the y-intercept...

Answer 26

to find the y-intercept, we set t = 0 and find f(t)

Answer 27

so i dont understand

Answer 28

the y intercept is out equation?

Answer 29

the y-intercept is a number, and to find that number, we find f(t) when t = 0

Answer 30

is that clear?

Answer 31

y-intercept = 0

Answer 32

so its just zero?

Answer 33

@vocaloid

Answer 34

yes

Answer 35

Oh, hah. thank you so much! :)

Answer 36

alright, but we're not done yet, now we need to find the intercept of g(t)

Answer 37

read the table, and tell me what g(t) equals when t = 0

Answer 38

oh goodness im not at this... uh 0 and 1.2?

Answer 39

im not good at this*

Answer 40

i dont know

Answer 41

look at the table again

look at the row where t = 0
what number is on the right hand side?

Answer 42

0

Answer 43

good, so the y-intercept of g(t) is 0

Answer 44

okay.

Answer 45

anything else?

Answer 46

ok, it also asks you to explain what the y-intercepts mean in the context of the problem

we know that t represents time, so when t = 0, time = 0 seconds

f(t) represents the height of the labrador, and g(t) represents the height of the foxhound

since both y-intercepts are 0, that means that both dogs start off at a height of 0

Answer 47

that should be it for the problem

Answer 48

Thank you!!