This an Algebra 2 lesson Introducing solving quadratic inequalities. Students have learned extensively about quadratics and should bring a little prior knowledge concerning basic concepts of the inequality relation. This lesson uses two classrooms and measuring tape.

1. Warm-up 1
What is the area of Mr. Paul’s
room in square meters?

2. Warm-up 2: key words and symbols used in inequalities
• Greater than
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3. Solving Quadratic
Inequalities
What it means to be less than a function

4. FYI: Aligned Common Core State Standards
CCSS: Mathematics, CCSS: HS: Algebra, Creating Equations
HSA-CED.A. Create equations that describe numbers or relationships
HSA-CED.A.1. Create equations and inequalities in one variable and use
them to solve problems. Include equations arising from linear and
quadratic functions, and simple rational and exponential functions.

5. Modeling with quadratic functions
Certain events are accurately modeled by quadratic functions. For
example:
• Area
• Projectiles (objects shot up into the air which are
pulled down by gravity)
• Profit and loss

6. Area
Ms. Ilonka wants her room to be increased in
size by at least 20 square meters. She wants
to increase the length and the width by the
same amount. To model this, we need to
know the dimensions of her room and then
figure out by how much we need to increase
the length and width.

7. Area – from blue to red

8. Area – how many square meters
is Ms. Ilonka’s room?

9. Area – how many square meters
is Ms. Ilonka’s room?

10. Area - modeling the situation
The function that describes the area of a
rectangle is a quadratic function

11. Area – “at least”
We can write a quadratic equation to show the
area of a rectangle
We can write a quadratic inequality to show if the
area must be at least 20 square meters more
than the original area

12. Projectile
Throw a ball forward and up and observe the
shape it makes. How do you think we can model
this with a quadratic curve?

13. Projectile
Let 푓 푥 = −푥2 + 4푥 + 5 be the model for
throwing a ball. The independent variable is time
in seconds and the dependent variable is vertical
distance in feet. During what time will the ball be
at least 8 ft high?

14. Projectile
Let 푓 푥 = −푥2 + 4푥 + 5 be the model for throwing a
ball. The independent variable is time in seconds and
the dependent variable is vertical distance in feet.
During what time will the ball be at least 8 ft high?
Step 1: graph the function

15. Projectile
Let 푓 푥 = −푥2 + 4푥 + 5 be the model for throwing a
ball. The independent variable is time in seconds and
the dependent variable is vertical distance in feet.
During what time will the ball be at least 8 ft high?
Step 1: graph the function (scale and label)
Step 2: draw a horizontal line at 8 ft

16. Projectile
Let 푓 푥 = −푥2 + 4푥 + 5 be the model for throwing a
ball. The independent variable is time in seconds and
the dependent variable is vertical distance in feet.
During what time will the ball be at least 8 ft high?
Step 1: graph the function (scale and label)
Step 2: draw a horizontal line at 8 ft
Step 3: Draw two vertical lines where your
horizontal line intersected the quadratic curve

17. Projectile
Let 푓 푥 = −푥2 + 4푥 + 5 be the model for throwing a ball.
The independent variable is time in seconds and the
dependent variable is vertical distance in feet. During what
time will the ball be at least 8 ft high?
Step 1: graph the function (scale and label)
Step 2: draw a horizontal line at 8 ft
Step 3: Draw two vertical lines where your horizontal
line intersected the quadratic curve
Step 4: write an inequality based on the x-values
(time interval in seconds)

18. Class time practice
Complete the problems from the textbook
Write the problem, each step and the solution in your notebook
p.114 #18-23
Then some word problems 
p.114 # 11 & p.115 #47

19. Out of class practice - homework 
p.116 #52, 53, 56, 62-65