Graphing Quadratic Functions in Context

In this video, Mrs. Ruccio reviews graphing quadratic functions using technology. The first example involves graphing a quadratic function representing an object's motion, focusing on identifying the vertex and interpreting the graph. The second example models the area of a garden, emphasizing the importance of scale and understanding the vertex's meaning. Throughout, viewers are encouraged to pause and graph along, ensuring comprehension of key concepts like initial height, maximum height, and intervals of increase.

What is the purpose of using technology in graphing quadratic functions?

• To eliminate the need for understanding the function

• To make the process faster

• To help visualize parabolas and their properties

• To avoid manual calculations

When graphing the quadratic function for the object's height, what should you use instead of 't'?

• z

• w

• y

• x

What shape should the graph of the quadratic function representing the object's height resemble?

• An upside-down U

• A circle

• A square

• A straight line

What is the initial height of the object in Example 1?

• 144 feet

• 128 feet

• 0 feet

• 80 feet

At what time does the object hit the ground in Example 1?

• 6 seconds

• 5 seconds

• 3 seconds

• 2 seconds

What is the maximum height reached by the object in Example 1?

• 80 feet

• 160 feet

• 144 feet

• 128 feet

In Example 2, what does the vertex of the graph represent?

• The time taken to plant the garden

• The minimum width of the garden

• The maximum area of the garden

• The initial area of the garden

Why is it important to adjust the scale when graphing the quadratic function in Example 2?

• To make the graph look more colorful

• To ensure the graph fits within the viewing window

• To change the shape of the graph

• To avoid using the calculator

What is the width of the garden when the area is at its maximum in Example 2?

• 11 feet

• 5 feet

• 7 feet

• 9 feet

What is the area of the garden when the width is 5 feet in Example 2?

• 150 feet squared

• 180 feet squared

• 130 feet squared

• 162 feet squared