Alg1 Lesson 3.10: Pursuit Problems

Lesson 3.10: Pursuit Problems

Obj: 8A, 8B: I can solve systems of quadratic
equations.

EQ: How do I solve a system of quadratic equations?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas and prior info
● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

Which part would you least like to play?

• Includer

• Facilitator

• Scribe

• Resourcer

● Check off tasks & skills on calendar.

● Select skills to work on.

● Work on Deltamath.

Remember to work on the following too…

Part 1: A Different Kind of

System of Equations

Compare & Contrast these Two Functions:

f(x) = x² - 5x + 6
g(x) = 3x - 10

Without graphing or solving, how many
intersections do you think there will be?

Fill in the Blank

Find the discriminant of x² - 5x + 6 = 3x - 10.

Multiple Choice

Find the intersection of f(x) = x² - 5x + 6 and g(x) = 3x - 10

• (4, 0)

• (4, 2)

• (1, 0)

• (6, 8)

Coefficient Relationship to Intersections

f(x) = x² - 5x + 6

g(x) = 3x - 10

What happens when you change the coefficients of the
functions? (Change one coefficient at a time and see
how it changes the intersections)

Desmos Graph:
https://www.desmos.com/calculator/v7cmjuwrhe

Part 2: The Cheetah and

the Wildebeest

Poll

Which of the following best describes your diet?

• Mostly herbivore

• Mostly carnivore

• Omnivore

A cheetah is hunting a wildebeest on the African plains. At time t = 0
seconds, the cheetah is 100 meters behind the wildebeest and is running
at a constant speed of 30 meters per second. At t = 0, the wildebeest
notices the cheetah and begins running faster and faster. In fact, the
wildebeest’s movement is modeled by W(t) = 2.5t², where W(t) measures
the distance from the wildebeest’s starting point t seconds after the
wildebeest noticed the cheetah. Will the cheetah catch the wildebeest?

To help solve, find:

●

Reasonable domain & range

●

Function to represent the
cheetah’s movement

Multiple Choice

What are the input and output quantities in this context?

• Distance traveled (D) is a function of time (t). t(D)

• Distance traveled (D) is a function of time (t). D(t)

• Time traveled (t) is a function of distance (D). D(t)

• Time traveled (t) is a function of distance (D). t(D)

Drag and Drop

What would make sense to use as the units of measurement for the
axes? ​

Placeholder

(in ​

Placeholder

) for the x-axis and ​

Placeholder

​

Placeholder

’s
starting point (in ​

Placeholder

) for the y-axis.

Drag these tiles and drop them in the correct blank above

Time

seconds

distance from the

wildebeest

meters

cheetah

years

miles

Multiple Select

Which quadrants would be used to solve this problem?

• QI

• QII

• QIII

• QIV

• QVI

Multiple Choice

What do you know about the cheetah’s speed?

• The cheetah’s speed is constant at
  30 meters per second.

• The cheetah runs at 25 meters per second.

• The cheetah’s speed is accelerating at
  60 miles per second.

• The cheetah will slow down because of a tourist trap.

Multiple Choice

What type of function could represent the cheetah’s speed?

• Quadratic

• Linear

• Exponential

Fill in the Blank

What is the slope of the cheetah function?

Fill in the Blank

What is the y-intercept of the cheetah function? (0, ___)

-

Multiple Choice

What algebraic expression might be a good representative of the cheetah’s distance in terms of elapsed time?

• C(t) = 30t + 100

• C(t) = 30t - 100
• C(t) = 100t + 30

• C(t) = -100t + 30

Multiple Choice

What key feature of the graph would let your know that the cheetah catches the wildebeest?

• The cheetah runs faster than the wildebeest.
• The functions W(t)'s and C(t)'s t-intercepts.

• The wildebeest starts moving backward.
• The functions W(t) and C(t) would intersect.

Do these Polynomials ever intersect?

W(t) = 2.5t²

C(t) = 30t - 100

No, here are the algebraic steps:

Part 3: Extending the

Problem

How could the Cheetah catch the Wildebeest?

Understanding the wildebeest’s position function really
requires some knowledge of physics or calculus.
The “2.5” in W(t) = 2.5t² means that the wildebeest
is accelerating at a constant 5 meter per
second squared. For this context, it is most important
to be able to adjust parameters and determine
graphically and algebraically whether the
wildebeest gets caught. What parameters could the
cheetah change to be able to catch the wildebeest?

Fill in the Blank

Without changing any other parameter, what is the farthest away (in meters) the cheetah could start and still catch the wildebeest?

__ meters

Fill in the Blank

Without changing any other parameter, how fast (in meter per second), would the cheetah need to be running to catch the wildebeest? __.__m/sec^2

.

Multiple Choice

The wildebeest’s position is given by W(t)= 2.5t^2. The parameter 2.5 tells us how fast the wildebeest is moving. If the cheetah runs at 30 meters per second from 100 meters behind the wildebeest, what is the lowest value the wildebeest’s parameter can be for the wildebeest to escape?

• 2.00

• 2.5

• 2.25

• 2.15

Part 4: Summary and

Practice

Handout 3.10: Pursuit Practice Problems

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.