Increasing and Decreasing Intervals of a Parabola

The intervals of increase and decrease describe the xx in which the parabola goes up and those in which it goes down.
Let's see it in an illustration:

B4 - The areas of increase and decrease describe the X where the parabola increases decreases

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.

Suggested Topics to Practice in Advance

  1. The quadratic function
  2. Parabola
  3. Plotting the Quadratic Function Using Parameters a, b and c
  4. Finding the Zeros of a Parabola
  5. Positive and Negative intervals of a Quadratic Function

Practice Increasing and Decreasing Domain of a Parabola

Examples with solutions for Increasing and Decreasing Domain of a Parabola

Exercise #1

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:

BBBAAACCC

Video Solution

Step-by-Step Solution

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.

Answer

x > C

Exercise #2

Based on the data in the graph

Identify the domain where the function increases:

000

Video Solution

Answer

x < 0

Exercise #3

Based on the data in the graph

Identify the domain where the function increases:

000

Video Solution

Answer

x > 0

Exercise #4

Based on the data in the graph

Identify the domain where the function is decreasing:

000

Video Solution

Answer

x > 0

Exercise #5

Based on the data in the graph

Identify the domain where the function is decreasing:

555

Video Solution

Answer

x > 5

Exercise #6

Based on the data in the graph

Identify the domain where the function is decreasing:

-7-7-7

Video Solution

Answer

x > -7

Exercise #7

Based on the data in the graph

Identify the domain where the function is decreasing:

000

Video Solution

Answer

x < 0

Exercise #8

Based on the data in the graph

Identify the domain where the function is increasing:

-2-2-2000

Video Solution

Answer

x < 0

Exercise #9

Based on the data in the graph

Identify the domain where the function is increasing:

-7-7-7

Video Solution

Answer

x < -7

Exercise #10

Based on the data in the graph

Identify the domain where the function is increasing:

555

Video Solution

Answer

x > 5

Exercise #11

Based on the data in the graph

Identify the domain with the decreasing function:

-2-2-2000

Video Solution

Answer

x > 0

Exercise #12

Based on the data in the graph

Identify the domain with the decreasing function:

777111444

Video Solution

Answer

x < 4

Exercise #13

Based on the data in the sketch below

Identify the domain where the function is increasing:

555

Video Solution

Answer

x < 5

Exercise #14

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:

XXXAAA

Video Solution

Answer

x > A

Exercise #15

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:

AAA

Video Solution

Answer

x > A

Topics learned in later sections

  1. Vertex of a parabola
  2. Symmetry in a parabola