Graphing Linear & Quadratic Functions Challenge for 9th Grade

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) based on the number of miles (m) driven. How much would it cost to drive 150 miles?

• $80

• $100

• $60

• $120

A ball is thrown into the air, and its height (h) in meters after t seconds is given by the equation h = -5t^2 + 20t + 1. Graph this quadratic function and determine the maximum height the ball reaches.

• 19 meters

• 25 meters

• 15 meters

• 21 meters

A store sells two types of tickets for a concert: regular tickets for $30 and VIP tickets for $50. If the total revenue from selling x regular tickets and y VIP tickets is $2000, write a linear equation to represent this situation. How many of each type of ticket could be sold if 40 regular tickets were sold?

• 30 regular tickets and 20 VIP tickets

• 20 regular tickets and 30 VIP tickets

• 40 regular tickets and 16 VIP tickets

• 50 regular tickets and 10 VIP tickets

The path of a projectile is modeled by the equation h = -4.9t^2 + 20t, where h is the height in meters and t is the time in seconds. Graph this quadratic function and find the time when the projectile hits the ground.

• Approximately 2.5 seconds

• Approximately 6.0 seconds

• Approximately 4.08 seconds

• Approximately 3.2 seconds

A farmer has a rectangular field with a length that is 3 meters longer than its width. If the area of the field is 70 square meters, write a quadratic equation to represent the relationship between the width (w) and the length. What are the dimensions of the field?

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

A company produces and sells x units of a product at a price of p = 100 - 2x. The cost to produce x units is given by C = 20x + 100. Write the profit function and determine the number of units that must be sold to maximize profit.

• 20

• 15

• 25

• 30

A quadratic function models the height of a water fountain over time: h(t) = -2t^2 + 8t + 5. Graph this function and find the time when the fountain reaches its maximum height.

• The fountain reaches its maximum height at t = 3 seconds.

• The fountain reaches its maximum height at t = 2 seconds.

• The fountain reaches its maximum height at t = 4 seconds.

• The fountain reaches its maximum height at t = 1 second.

Two friends are jogging on a straight path. One jogs at a speed of 4 km/h, and the other jogs at a speed of 6 km/h. If they start at the same point, write a linear equation to represent the distance each friend has jogged after t hours. How far apart will they be after 2 hours?

• 8 km

• 2 km

• 4 km

• 10 km

A rectangular garden has a length that is twice its width. If the area of the garden is 48 square meters, write a quadratic equation to find the dimensions of the garden. What are the length and width?

• Width: 6 meters, Length: 12 meters

• Width: 3 meters, Length: 6 meters

• Width: 5 meters, Length: 10 meters

• Width: 4.9 meters, Length: 9.8 meters

A local theater sells tickets for $15 for adults and $10 for children. If the total revenue from selling x adult tickets and y child tickets is $1200, write a linear equation to represent this situation. If 30 adult tickets were sold, how many child tickets were sold?

• 60

• 90

• 75

• 45