Quadratic Functions and Regression

The video tutorial covers quadratic regression, explaining how to model data with quadratic equations and solve problems using regression equations. It demonstrates using TI-84 and Desmos calculators to find the curve of best fit through examples like a baseball trajectory, a cliff jump, and a pumpkin launch. The tutorial also discusses finding maximum heights and predicting values using the regression equations.

What is the primary purpose of quadratic regression?

• To find the mean of a data set

• To model data with a quadratic equation

• To calculate the standard deviation

• To model data with a linear equation

Which calculators are mentioned for use in quadratic regression?

• Casio and Desmos

• HP and TI-84

• TI-84 and Desmos

• TI-89 and Casio

What is the first step in performing quadratic regression on a TI-84?

• Calculate the mean

• Enter data into L1 and L2

• Press the graph button

• Use the quadratic formula

In the baseball example, what is the equation for the curve of best fit?

• y = x^2 - 0.08x + 3

• y = 0.08x^2 - x + 3

• y = -x^2 + 0.08x + 3

• y = -0.08x^2 + x + 3

What is the maximum height of the baseball according to the graph?

• 8.125 feet

• 6.125 feet

• 5.125 feet

• 7.125 feet

How high is the baseball when it is 10 meters away from home plate?

• 4 feet

• 5 feet

• 6 feet

• 7 feet

What is the equation for the curve of best fit in the cliff jump example?

• y = -16x^2 + 18x + 480

• y = -18x^2 + 16x + 480

• y = 16x^2 - 18x + 480

• y = 18x^2 - 16x + 480

How long does it take Casey to reach a height of 150 feet?

• 5.139 seconds

• 4.139 seconds

• 6.139 seconds

• 7.139 seconds

What is the equation for the curve of best fit in the pumpkin launching example?

• y = 16x^2 - 40x + 2

• y = 40x^2 - 16x + 2

• y = -40x^2 + 16x + 2

• y = -16x^2 + 40x + 2

What does the vertex represent in the pumpkin launching example?

• The average height of the pumpkin

• The time it takes to reach the ground

• The maximum height of the pumpkin

• The starting height of the pumpkin