Graphing Quadratic Equations to Solve Real World Problems

This lesson teaches how to solve real-world problems using graphs of quadratic equations. It covers key features of parabolas, such as zeros, vertex, and axis of symmetry. The lesson explains the importance of considering only positive zeros in time-related problems. Two example problems are analyzed: one involving a water balloon and another involving a ball, demonstrating how to determine the time in the air and maximum height using graphs. The lesson concludes with a summary of the problem-solving process using quadratic graphs.

What are the key features of a quadratic graph?

• Amplitude, frequency, and phase shift

• Slope, intercept, and curvature

• Mean, median, and mode

• Zeroes, vertex, and axis of symmetry

In the context of quadratic graphs, what is a common misunderstanding about zeroes?

• Zeroes determine the axis of symmetry

• All zeroes are solutions to the problem

• Zeroes are always positive

• Zeroes are the same as the vertex

In the water balloon problem, why can't the negative zero be used?

• The graph does not intersect the x-axis

• The vertex is at a negative point

• Time cannot be negative

• The balloon never reaches the ground

How long was the water balloon in the air according to the graph?

• 3 seconds

• 5 seconds

• 9 seconds

• 7 seconds

What was the maximum height reached by the ball in the ball throw problem?

• 5 feet

• 7 feet

• 9 feet

• 11 feet