Warm-up 1

What is the area of Mr. Paul’s room in square meters?

Warm-up 2: key words and symbols used in inequalities

• Greater than

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Solving Quadratic Inequalities

What it means to be less than a function

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.

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

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.

Area – from blue to red

Area – how many square metersis Ms. Ilonka’s room?

Area – how many square metersis Ms. Ilonka’s room?

Area - modeling the situation

The function that describes the area of a rectangle is a quadratic function

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

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?

Projectile

Let 𝑓 𝑥 = −𝑥2 + 4𝑥 + 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?

Projectile

Let 𝑓 𝑥 = −𝑥2 + 4𝑥 + 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

Projectile

Let 𝑓 𝑥 = −𝑥2 + 4𝑥 + 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

Projectile

Let 𝑓 𝑥 = −𝑥2 + 4𝑥 + 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

Projectile

Let 𝑓 𝑥 = −𝑥2 + 4𝑥 + 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 ftStep 3: Draw two vertical lines where your horizontal line intersected the quadratic curveStep 4: write an inequality based on the x-values (time interval in seconds)

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

Out of class practice - homework

p.116 #52, 53, 56, 62-65