Find the positive and negative domains of the function below:
We have hundreds of course questions with personalized recommendations + Account 100% premium
Find the positive and negative domains of the function below:
The function given is , which is a downward-opening parabola because the coefficient of the squared term () is negative.
The vertex form tells us the vertex of the parabola is at .
The function will be zero where . Solving this equation, we set:
Taking the square root of both sides gives:
Thus, and .
These are the roots of the quadratic, splitting the domain into three intervals: , , and .
We need to test the sign of in each interval:
After analyzing these intervals, the function is positive for and negative otherwise.
Therefore, the positive and negative domains of the function are as follows:
or
or
The graph of the function below intersects the X-axis at points A and B.
The vertex of the parabola is marked at point C.
Find all values of \( x \) where \( f\left(x\right) > 0 \).
Get unlimited access to all 18 The Quadratic Function questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime