The intervals of increase and decrease describe the in which the parabola goes up and those in which it goes down.
Let's see it in an illustration:
We must always observe the function from left to right.
When we see a negative slope (this is how decrease looks) – the function is decreasing.
When we see a positive slope (this is how increase looks) – the function is increasing.
The parabola will change interval only at one point - at the vertex of the parabola.
Note that the graph of the function intersects the x-axis at points A and B
Moreover the vertex of the parabola is marked at point C
Identify the segment below where the function increases:
Note that the graph of the function shown below does not intersect the x-axis
The parabola's vertex is A
Identify the interval where the function is decreasing:
Note that the graph of the function intersects the x-axis at points A and B
Whilst the vertex of the parabola is marked at point C
Identify the segment below where the function is increasing:
Note that the graph of the function intersects the x-axis at points A and B
Moreover the vertex of the parabola is marked at point C
Identify the segment where the function is decreasing:
Note that the graph of the function intersects the x-axis at points A and B
Moreover the vertex of the parabola is marked at point C
Identify the segment below where the function is decreasing:
Note that the graph of the function intersects the x-axis at points A and B
Moreover the vertex of the parabola is marked at point C
Identify the segment below where the function increases:
From the graph we can see that the parabola is a smiling parabola,
meaning that its extreme point is a minimum point.
If we describe it in words, until the extreme point the function decreases,
after the extreme point it increases.
Since we measure the progress using X,
we can say that the function increases whenever X is greater than point C, the extreme point.
Mathematically we can write:
X>C
As we already said, as long as X is greater than C, the function increases.
x > C
Note that the graph of the function shown below does not intersect the x-axis
The parabola's vertex is A
Identify the interval where the function is decreasing:
x < A
Note that the graph of the function intersects the x-axis at points A and B
Whilst the vertex of the parabola is marked at point C
Identify the segment below where the function is increasing:
x < C
Note that the graph of the function intersects the x-axis at points A and B
Moreover the vertex of the parabola is marked at point C
Identify the segment where the function is decreasing:
x > C
Note that the graph of the function intersects the x-axis at points A and B
Moreover the vertex of the parabola is marked at point C
Identify the segment below where the function is decreasing:
x < C
Note that the graph of the function below intersects the x-axis at point - A which is the vertex of the parabola where the function is tangent to the x-axis
Identify the interval where the function is increasing:
Note that the graph of the function below intersects the x-axis at A which is the vertex of the parabola where the function is tangent to the x-axis
Identify the interval where the function is decreasing:
Note that the graph of the function below does not intersect the x-axis
Moreover the parabola's vertex is A
Identify the interval where the function is increasing:
Note that the graph of the function below does not intersect the x-axis
Moreover the parabola's vertex is A
Identify the interval where the function is decreasing:
Note that the graph of the function below does not intersect the x-axis
Moreover the parabola's vertex is A
Identify the interval where the function is increasing:
Note that the graph of the function below intersects the x-axis at point - A which is the vertex of the parabola where the function is tangent to the x-axis
Identify the interval where the function is increasing:
x > A
Note that the graph of the function below intersects the x-axis at A which is the vertex of the parabola where the function is tangent to the x-axis
Identify the interval where the function is decreasing:
x < A
Note that the graph of the function below does not intersect the x-axis
Moreover the parabola's vertex is A
Identify the interval where the function is increasing:
x < A
Note that the graph of the function below does not intersect the x-axis
Moreover the parabola's vertex is A
Identify the interval where the function is decreasing:
x > A
Note that the graph of the function below does not intersect the x-axis
Moreover the parabola's vertex is A
Identify the interval where the function is increasing:
x > A
Based on the data in the graph
Identify the domain where the function is increasing:
Based on the data in the graph
Identify the domain where the function is decreasing:
Based on the data in the graph
Identify the domain where the function is increasing:
Based on the data in the graph
Identify the domain where the function is decreasing:
Based on the data in the graph
Identify the domain where the function increases:
Based on the data in the graph
Identify the domain where the function is increasing:
x > 5
Based on the data in the graph
Identify the domain where the function is decreasing:
x > -7
Based on the data in the graph
Identify the domain where the function is increasing:
x < -7
Based on the data in the graph
Identify the domain where the function is decreasing:
x < 0
Based on the data in the graph
Identify the domain where the function increases:
x > 0