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Interpret Quadratic Functions from Graphs and Tables

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Lesson Plans and Worksheets for Algebra I
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More Lessons for Algebra I
Common Core For Algebra I

Examples, solutions, and videos to help Algebra I students learn how to interpret quadratic functions from graphs and tables: zeros ( x-intercepts), y-intercept, the minimum or maximum value (vertex), the graph's axis of symmetry, positive and negative values for the function, increasing and decreasing intervals, and the graph's end behavior.

Students determine an appropriate domain and range for a function's graph and when given a quadratic function in a context, recognize restrictions on the domain.

New York State Common Core Math Algebra I, Module 4, Lesson 10

Worksheets for Algebra I, Module 4, Lesson 10 (pdf)

Lesson 10 Summary

When interpreting quadratic functions and their graphs, it is important to note that the graph does not necessarily depict the path of an object. In the case of free-falling objects, for example, it is height with respect to time.

The y-intercept can represent the initial value of the function given the context, and the vertex represents the highest (if a maximum) or the lowest (if a minimum) value.

Opening Exercise:
Dolphins Jumping In and Out of the Water

Watch the following video clip of the dolphins jumping in and out of the ocean.

Example 1

In a study of the activities of dolphins, a marine biologist made a 24-second video of a dolphin swimming and jumping in the ocean with a specially equipped camera that recorded one dolphin’s position with respect to time. This graph represents a piecewise function, f(t), that is defined by quadratic functions on each interval. It relates the dolphin’s vertical distance from the surface of the water, in feet, to the time from the start of the video, in seconds. Use the graph to answer the questions below.

What happens at f(t) = 0?
What does f(t) = 0.50 means?
How long was Flipper under the water?
What was the maximum height Flipper reached?
How long was Flipper above the water?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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