Modeling Movie Prices with Quadratics

Christine, working in a movie store, documents movie prices and their release years. She analyzes the data to find a model that best fits the trend, which is decreasing and convex. Two models are considered: an exponential and a quadratic. The quadratic model is found to be a better fit as it balances overestimation and underestimation more effectively. Using this model, Christine predicts the price of a movie released 5.5 years ago, calculating it to be approximately 63 cents.

What information did Christine document about each movie title?

• The price and years since release

• The genre and director of the movie

• The box office earnings

• The number of awards won

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CCSS.HSF-LE.A.1B

What type of trend did Christine observe in her data?

• Constant and linear

• Fluctuating and random

• Decreasing and convex

• Increasing and concave

Which two types of models did Christine consider for her data?

• Linear and logarithmic

• Polynomial and sinusoidal

• Exponential and quadratic

• Logarithmic and sinusoidal

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CCSS.HSF-IF.C.7A

What characteristic of the data trend indicates a convex shape?

• The curve opens upwards

• The curve is a zigzag pattern

• The curve is a straight line

• The curve opens downwards

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CCSS.HSF.LE.A.4

What is the main issue with the exponential model according to the analysis?

• It underestimates the price for most data points

• It overestimates the price for all data points

• It perfectly fits all data points

• It is not a decreasing function

Which model was determined to be a better fit for the data?

• Neither model fits the data

• Both models fit equally well

• The quadratic model

• The exponential model

How does the quadratic model balance overestimation and underestimation?

• It only overestimates the prices

• It only underestimates the prices

• It neither overestimates nor underestimates

• It balances both overestimation and underestimation

What is the predicted price of a movie released 5.5 years ago using the quadratic model?

• 50 cents

• 75 cents

• 80 cents

• 63 cents

What is the formula used in the quadratic model for price prediction?

• y = x^2 + 2x + 5

• y = 3x^2 - 4x + 10

• y = 2x^2 + 3x - 7

• y = 0.5x^2 - 5x + 13

Why is it important to round the predicted price to the nearest cent?

• To simplify the model

• To avoid decimal errors

• To match the currency format

• To make the calculation easier