Introduction to Parabolas

1. A, C and D

There are two pairs of statements. Each pair is about a different property:

1. The first pair is about the amount of rainfall when there's the largest possible number of mosquitoes. The $x$-coordinate of the vertex represents this.
2. The second pair is about the amount of rainfall when there are no mosquitoes. The parabola's $x$-intercepts represent this.

The amount of rainfall when there's the largest possible number of mosquitoes

Let's look at the $x$-coordinate of the vertex.

We can see that the $x$-coordinate at the vertex is about $2$.

The conditions for no mosquitoes

Let's look at the $x$-intercepts.

We can see that the parabola intersects the $x$-axis both when rainfall is $0$ and when it's $4 \text{ cm}$.

Answers

There are three correct statements:

• There's the largest possible number of mosquitoes when rainfall is about $2 \text{ cm}$.
• There are no mosquitoes when there is no rainfall.
• There are no mosquitoes when rainfall is about $4 \text{ cm}$.

2. A and C

There are two pairs of statements. Each pair is about a different property:

1. The first pair is about the conditions for this behavior: "Greater width relates to greater area." This is a description of an increasing function.
2. The second pair is about the width when the area is the greatest possible. The \x\)-coordinate of the vertex represents this.

The conditions for "Greater width relates to greater area"

Let's see where the function increases.

We can see that the function increases when the width is less than $10\text{ m}10$.

The width when the area is the greatest possible

Let's look at the $x$-coordinate of the vertex.

We can see that the width at the vertex is about $10\text{ m}$.

Answers

There are two correct statements:

• Greater width relates to greater area as long as the width is less than $10\text{ m}$.
• To get the greatest area, the width should be $10\text{ m}$.

3. B and C

There are two pairs of statements. Each pair is about a different property:

1. The first pair is about the company's profit if they don't charge for their app. The $/y$-intercept represents this.
2. The second pair is about the app price that will bring the company the greatest profit. The $x$-coordinate of the vertex represents this.

The company's profit if they don't charge for their app

Let's look at the $y$-intercept.

We can see that the profit at the $y$-intercept is about $-10$ million dollars.

The app price that will bring the company the greatest profit

Let's look at the $x$-coordinate of the vertex.

We can see that the price at the vertex is about $7$ dollars.

Answers

There are two correct statements:

• If the company doesn't charge for the app, they lose about $10$ million dollars.
• To make the greatest profit, the company should charge $7$ dollars for the app.

4. C

There are two pairs of statements. Each pair is about a different property:

1. The first pair is about the time period when the ball moved upwards. This is a description of an increasing function.
2. The second pair is about the time it took the ball to hit the ground. The second $x$-intercept represents this.

The time period when the ball moved upwards

Let's see where the function increases.

We can see that the function increases until about $1.75\text{ s}$, not after it, and not for $3.5\text{ s}$.

The time it took the ball to hit the ground

Let's look at the $x$-intercept.

We can see that time at the $x$-intercept is about $3.5\text{ s}$.

Answers

There is only one correct statement:

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