Math Problem Statement

During which interval is the function shown on the graph below decreasing?

Solution

To determine the interval where the function shown on the graph is decreasing, we need to observe the behavior of the function as xx moves from left to right.

From the graph:

  1. The function is a parabola opening upwards, which is characteristic of a quadratic function with a minimum point at the vertex.
  2. The function decreases as xx moves from -\infty up to the vertex and then increases afterward.
  3. The vertex of the parabola is located at x=2x = -2.

Therefore, the interval during which the function is decreasing is: (,2)(-\infty, -2)

The correct answer is: A. (,2)(-\infty, -2)

Would you like more details or have any questions?

Here are some related questions for further exploration:

  1. How do you determine the intervals of increase and decrease for other types of functions?
  2. What is the significance of the vertex in determining the behavior of a quadratic function?
  3. How can you determine the vertex of a quadratic function from its equation?
  4. How does the direction in which a parabola opens affect the intervals of increase and decrease?
  5. What methods can be used to find the vertex without graphing the function?

Tip: To find the vertex of a quadratic function f(x)=ax2+bx+cf(x) = ax^2 + bx + c, you can use the formula x=b2ax = -\frac{b}{2a} to determine the x-coordinate of the vertex.

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Math Problem Analysis

Mathematical Concepts

Functions
Intervals of Increase and Decrease
Quadratic Functions

Formulas

The vertex form of a quadratic function y = ax^2 + bx + c
Interval notation for increase/decrease

Theorems

Concept of vertex as a minimum or maximum point in a parabola

Suitable Grade Level

Grades 8-10