Increasing and Decreasing Domain of a Parabola: Graphical representation

Examples with solutions for Increasing and Decreasing Domain of a Parabola: Graphical representation

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

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:

XXXAAA

Video Solution

Answer

x < A

Exercise #3

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:

AAABBBCCC

Video Solution

Answer

x < C

Exercise #4

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:

AAABBBCCC

Video Solution

Answer

x > C

Exercise #5

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:

BBBAAACCC

Video Solution

Answer

x < C

Exercise #6

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:

AAA

Video Solution

Answer

x > A

Exercise #7

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:

AAA

Video Solution

Answer

x < A

Exercise #8

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:

XXXAAA

Video Solution

Answer

x < A

Exercise #9

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 #10

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