Modeling with Quadratic Functions

The video tutorial by Kirk Wier covers modeling with quadratic functions, focusing on real-world applications. It includes exercises on projectile motion, modeling a skateboard ramp, and finding optimal popcorn popping temperatures. The tutorial emphasizes understanding quadratic equations, graphing, and solving inequalities graphically. The session concludes with a discussion on the importance of quadratic functions in various real-world scenarios.

What is the primary focus of the lesson on modeling with quadratic functions?

• Exploring linear functions

• Studying exponential functions

• Understanding quadratic functions and their real-world applications

• Learning about trigonometric functions

In Exercise 1, what is the initial height of the object when it is fired?

• 10 feet

• 50 feet

• 0 feet

• 100 feet

What shape does the graph of the object's height over time take?

• A concave up parabola

• A circle

• A concave down parabola

• A straight line

How is the maximum height of the object determined algebraically?

• By graphing the equation

• Using the formula B/2A

• By completing the square

• Using the quadratic formula

In Exercise 2, what does the variable X represent in the halfpipe model?

• The height of the ramp

• The width of the halfpipe

• The depth of the halfpipe

• The horizontal distance across the halfpipe

What is the height of the halfpipe at its endpoints?

• 7 feet

• 10 feet

• 5 feet

• 12 feet

In Exercise 3, what is the optimal temperature for popping the most kernels?

• 350°F

• 250°F

• 300°F

• 400°F

What percentage of kernels pop at the optimal temperature?

• 100%

• 96%

• 90%

• 85%

What is the range of temperatures that ensures at least 85% of kernels pop?

• 350°F to 450°F

• 200°F to 300°F

• 400°F to 500°F

• 298°F to 402°F