Hillsborough Rate of Change of The Equation in A Linear Format Questions

Need help with the attached pdf on understanding parameters. It is due within 2 hours please

Name: _______________________________
4.1 and 4.2 Understanding the Parameters a, b, and c
Let’s add some context so you understand the meaning of the value of the ‘a,’ ‘b,’ and ‘c’ in the
general form of the quadratic function 𝑓(𝒙) = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄. We will revisit the Willis Tower
problem…
1.
Suppose you throw a ball up into the air from the top of Willis Tower (old Sears Tower).
The model that represents the ball’s height as a function of how many seconds have passed
Bishop MAT 121
Name: ______________________________________
may be modeled by:
”
𝐻(𝑡)a =
+ air
40𝑡form
+ 1450
5) Suppose you throw
ball−16𝑡
up into the
the top of Willis Tower (old Sears
a.
Tower). The model that represents the
ball’susing
heightthe
as amodel.
function of how many
Fill in the table
seconds have passed may be modeled by:
H (t) = −16t 2 + 40t +1450
b.
Describe what the ∆𝐻 column tells us about
a) Fill in the table using the model
the situation. In other words, what does the first
difference tell us about the relationship between the
height and time?
b) Describe what the ΔH column tells
us about the situation
t
H(t)
ΔH
Δ(ΔH )
0
1
2
3
4
the Δ(ΔH)
c.
Describe what c)theDescribe
∆(∆𝐻)what
column
tells column
us
tells us
about the
situation
about the situation. In other
words,
what
does the
second difference tell us about the height and time?
d.
5
what
the a, b,tell
andyou
c value
tell you
the context
the situation
Describe what d)
theDescribe
a, b, and
c value
about
theabout
context
of theofsituation.
3
Name: _______________________________
4.1 and 4.2 Understanding the Parameters a, b, and c
In general, describe what the a, b, and c value tell you.
𝑓(𝒙) = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄
c value:
b value:
a value:
2.
Spotify is a music, podcast, and video streaming service. It was developed in Stockholm,
Sweden, and was officially launched on October 7, 2008. Since then it has posted very
impressive revenue reports. From 2009 through 2016, Spotify’s annual revenue can be
modeled by
𝑅(𝑡) = 76.9𝑡 ” − 148.9𝑡 + 99.7
where t represents the number of years since 2009 and R is Spotify’s revenue measured in
millions of euros.
Describe what the a, b, and c value tell you about Spotify’s revenue. Be specific!