Introduction to Parabolas

While the graph of a linear equation is a straight line, the graph of a quadratic equation is a curve called a parabola. Parabolas are more complicated to graph than lines, but they have distinct features and properties that you can use to help with graphing. This lecture series explores what all parabolas have in common and how to use them to model real-life situations. Watch the videos and complete the interactive exercises.

Interpret a quadratic graph

1. The function $g$ models the number of mosquitoes (in millions of mosquitoes) in a certain area as a function of rainfall (in centimeters) in that area.

Which of these statements are true?

Choose all answers that apply:

A. There's the largest possible number of mosquitoes when rainfall is about $2 \text { cm }$ .

B. There's the largest possible number of mosquitoes when rainfall is about $4 \text{ cm }$ .

C. There are no mosquitoes when there is no rainfall.

D. There are no mosquitoes when rainfall is about $4 \text{ cm}$ .

2. Simon has a certain length of fencing to enclose a rectangular area. The function $A$ models the rectangle's area (in square meters) as a function of its width (in meters).

Which of these statements are true?

Choose all answers that apply:

A. Greater width relates to greater area as long as the width is less than $10\text{ m}$ .

B. Greater width relates to greater area as long as the width is more than $10\text{ m}$ .

C. To get the greatest area, the width should be $10\text{ m}$ .

D. To get the greatest area, the width should be $20\text{ m}$ .

3. A certain company's main source of income is a mobile app. The function $h$ models the company's annual profit (in millions of dollars) as a function of the price they charge for the app (in dollars).

Which of these statements are true?

Choose all answers that apply:

A. If the company doesn't charge for the app, they make $0$ profit.

B. If the company doesn't charge for the app, they lose about $10$ million dollars.

C. To make the greatest profit, the company should charge $7$ dollars for the app.

D. To make the greatest profit, the company should charge $40$ dollars for the app.

4. Sarah kicked a ball in the air. The function $f$ models the height of the ball (in meters) as a function of time (in seconds) after Sarah kicked it.

Which of these statements are true?

Choose all answers that apply:

A. The ball moved upwards for about $3.5\text{ s}$ .

B. The ball started moving upwards after about $1.75\text{ s}$ .

C. The ball hit the ground after about $3.5\text{ s}$ .

D. The ball hit the ground after about $1.75\text{ s}$ .