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Lesson: Interpreting the Relative Maximum and Minimum and the End Behavior of a Graph

In this lesson, we will learn how to interpret the extrema and the end behavior of a given graph.

Question Video: Finding the Maximum or Minimum Value of a Quadratic Function

02:20

Worksheet: Interpreting the Relative Maximum and Minimum and the End Behavior of a Graph • 3 Questions

Q1:

Find the maximum or minimum value of the function , given .

  • A The minimum value is 1.
  • B The minimum value is 3.
  • C The maximum value is 1.
  • D The maximum value is 0.
  • E The minimum value is 0.

Q2:

Consider the graph of the quartic shown.

Which of the points , , and is a local maximum?

  • A
  • B
  • C

Which of the points , , and is a local minimum?

  • A and
  • B and
  • C and

Which of the points , , and is a global minimum?

  • A
  • B
  • C

By considering the end behavior of the quartic, determine whether the leading coefficient is positive or negative.

  • ANegative
  • BPositive

Q3:

Consider the cubic graph shown.

What are the coordinates of the local maximum?

  • A
  • B
  • C
  • D

What are the coordinates of the local minimum?

  • A
  • B
  • C
  • D

If we consider the end behavior of this cubic, it enters into the bottom left quadrant and exits from the top right quadrant. Is the leading coefficient of this cubic positive or negative?

  • ANegative
  • BPositive
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