# 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:

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
Therefore, the set of negativity of the function is: $-6

## Examples with solutions for Positive and Negative Domains

### Exercise #1

The following function is graphed below:

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

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

### Answer

For all values of x

### Exercise #2

The following function is graphed below:

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

For which values of x is

f(x)>0 true?

2 < x , x < 4

### Exercise #3

The following function is graphed below:

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

For which values of x is

f(x)>0 true?

No answer

### Exercise #4

The following function is graphed below:

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

For which values of x is

f(x)<0 true?

2 < x < 4

### Exercise #5

The following function is graphed below:

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

For which values of x is

f(x)>0 true?

-1 < x < 6

### Exercise #6

The following function is graphed below:

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

For which values of x is

f(x)<0 true?

### Answer

Answers (a) and (b)