Introduction to Parabolas

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 $1.75\text{ s}$.