Positive and Negative Domains - Examples, Exercises and Solutions

Positive and Negative intervals of a Quadratic Function

To find out when the parabola is positive and when it is negative, we must plot its graph.
Then we will look at
When the graph of the parabola is above the $X$ axis, with a positive $Y$ value, the set is positive
When the graph of the parabola is below the $X$ axis, with a negative $Y$ value, the set is negative
Let's see it in an illustration:

Representation of the Positive and Negative domains of a Quadratic Function

We will ask ourselves:
When is the graph of the parabola above the $X$ axis?
When $X>-1$ or $X<-6$
Therefore, the sets of positivity of the function are: $X>-1$ , $X<-6$
Now we will ask When is the graph of the parabola below the $X$ axis?
When $6<X<-1$
Therefore, the set of negativity of the function is: $-6<X<-1$

Practice Positive and Negative Domains

Question 1

The following function is graphed below:

$$ f(x)=-2x^2+4x-6 $$

For which values of x is
$$ f(x)<0 $$ true?

Question 2

The following function is graphed below:

$$ y=x^2-6x+8 $$

For which values of x is

$$ f(x)>0 $$ true?

Question 3

The following function is graphed below:

$$ f(x)=-2x^2+4x-6 $$

For which values of x is

$$ f(x)>0 $$ true?

Question 4

The following function is graphed below:

$$ y=-x^2+5x+6 $$

For which values of x is

$$ f(x)>0 $$ true?

Question 5

The following function is graphed below:

$$ y=-x^2+5x+6 $$

For which values of x is

Answers (a) and (b)

Question 1

The following function is graphed below:

$$ y=x^2-6x+8 $$

For which values of x is

$$ f(x)<0 $$ true?

Exercise #6

The following function is graphed below:

$y=x^2-6x+8$

For which values of x is

$f(x)<0$ true?

Video Solution

Answer

$2 < x < 4$

Positive and Negative Domains - Examples, Exercises and Solutions

Positive and Negative intervals of a Quadratic Function

Suggested Topics to Practice in Advance

Practice Positive and Negative Domains

Examples with solutions for Positive and Negative Domains

Exercise #1

Video Solution

Answer

Exercise #2

Video Solution

Answer

Exercise #3

Video Solution

Answer

Exercise #4

Video Solution

Answer

Exercise #5

Video Solution

Answer

Exercise #6

Video Solution

Answer

Topics learned in later sections