Modeling With Polynomial

Scenario 1: The population of a city is currently 50,000. It is estimated that the population will increase by 1,200 people each year. What is the polynomial equation to represent the population of the city as a function of the number of years since the current population count?

• P(t) = 50000 + 1200t

• P(t) = 50000 - 1200t

• P(t) = 50000t + 1200

• P(t) = 1200t - 50000

A concert venue charges $30 for each ticket sold. The number of tickets sold for a particular concert is represented by 'x'. Write a polynomial equation to represent the revenue generated from ticket sales as a function of the number of tickets sold.

• R(x) = 30x

• R(x) = 30 + x

• R(x) = 30x + 1

• R(x) = x - 30

The water level in a reservoir is decreasing at a constant rate of 0.3 meters per year. The initial water level is 10 meters. What is the polynomial equation to represent the water level in the reservoir as a function of the number of years since the initial measurement?

• W(t) = 10 + 0.3t

• W(t) = 10 - 0.3t

• W(t) = 0.3t - 10

• W(t) = 10t - 0.3

A ball is thrown into the air with an initial velocity of 30 meters per second. The height of the ball (in meters) can be modeled by the quadratic function h(t) = -5t² + 30t + 5, where t represents time in seconds. What is the maximum height the ball reaches?

• A) 45 meters

• B) 50 meters

• C) 55 meters

• D) 60 meters

A satellite dish is mounted on a wall. The height (in meters) of the satellite dish above the ground as it moves horizontally along a wall is given by the quadratic function h(x) = -0.1x² + 5x + 2, where x represents the horizontal distance from the starting point. What is the height of the satellite dish when it is 10 meters away from the starting point?

• 42 meters

• 45 meters

• 40 meters

• 55 meters

• 1000 t-shirts

• 1250 t-shirts

• 1500 t-shirts

• 1750 t-shirts

Which equations would BEST model the following data (select all that apply)

Find the Vertex: y= -5x² -20x - 26

• (-2, -6)

• (2, 6)

• (6,2)

• (3, 6)

Match the key words from real-world scenarios with the Quadratic Characteristic that it represents.

• Increases

• beginning height

• Zero

• Maximum Profit

• Decrease

• lands on the ground

• Vertex

• Rises

• Y-intercept

• Falls

Draw a quadratic function whose vertex is in the 2nd quadrant and has no zeros.