Calculating Firework Safety: Quadratic Inequalities and Heights

The video tutorial explains how to write and solve quadratic inequalities using a fireworks example. It introduces the vertical motion model, discusses graphing quadratic inequalities, and applies these concepts to determine the time range for fireworks to explode at a regulated height. The tutorial emphasizes understanding solutions through graphing and interpreting results in real-life scenarios.

What does the vertical motion model equation represent in the context of fireworks?

• The sound of the fireworks

• The height of the fireworks over time

• The speed of the fireworks

• The color of the fireworks

In the context of quadratic inequalities, what is a common misunderstanding when graphing?

• Using the wrong color for the graph

• Forgetting to include the inequality line

• Plotting the graph upside down

• Not labeling the axes

What is the minimum height required for fireworks to explode in the given scenario?

• 256 feet

• 512 feet

• 128 feet

• 64 feet

What is the initial velocity of the fireworks in the example provided?

• 32 feet per second

• 128 feet per second

• 256 feet per second

• 64 feet per second

When solving the quadratic inequality, what is the first step after rewriting it as an equation?

• Divide both sides by 16

• Add 256 to both sides

• Subtract 256 from both sides

• Multiply both sides by 16

What range of time (in seconds) is determined for the fireworks to explode at the regulated height?

• Between 1 and 2 seconds

• Between 2 and 4 seconds

• Between 3 and 5 seconds

• Between 5 and 7 seconds

Why is it important to check solutions using a number line when solving quadratic inequalities?

• To avoid using a calculator

• To ensure the graph is colorful

• To verify the range of solutions

• To make the process faster