Math Problem Statement
Solution
The graph depicts a parabola opening downwards, indicating a quadratic function. To determine where the function is decreasing, we need to look at the portion of the graph where the slope is negative (falling).
The graph reaches its maximum value at the vertex, which occurs at , where the function changes from increasing to decreasing. From this point onward, as increases, the function is decreasing.
Thus, the function is decreasing for , and looking at the graph, it decreases indefinitely towards the right, i.e., from to .
Therefore, the interval where the function is decreasing is:
Would you like more details or have any questions about this explanation?
Here are 5 related questions:
- What is the interval where the function is increasing?
- How do you find the vertex of a parabola algebraically?
- What is the significance of the vertex in a quadratic function?
- How do you determine intervals of increase or decrease from a graph without calculus?
- Can you identify the equation of this parabola from its graph?
Tip: When analyzing functions, the vertex of a parabola is a key point, marking the transition between increasing and decreasing intervals.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Quadratic Functions
Decreasing Intervals
Formulas
Quadratic function: ax^2 + bx + c
Vertex form of a quadratic function
Theorems
The Vertex Theorem for Quadratic Functions
Suitable Grade Level
Grades 8-10
Related Recommendation
Identifying Decreasing Intervals of a Quadratic Function on a Graph
Identifying Increasing and Decreasing Intervals of a Quadratic Function
Determining Increasing and Decreasing Intervals of a Quadratic Function
Determine Decreasing Intervals for a Quadratic Function from its Graph
Identify Decreasing Intervals of a Function from its Graph