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 $6<X<-1$
Therefore, the set of negativity of the function is: $-6<X<-1$

Positivity and Negativity Sets of the Parabola

Pay attention!
Do not confuse the intervals of increase and decrease with the sets of positivity and negativity.
The intervals of increase and decrease describe when the function is increasing or decreasing, regardless of its position, above or below the $X$ axis.
On the other hand, the sets of positivity and negativity describe when the function is positive - above the $X$ axis or negative - below the $X$ axis, regardless of whether the function is increasing or decreasing.

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