Find the positive and negative domains of the function:
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Find the positive and negative domains of the function:
To find the positive and negative domains of the function , we'll follow these steps:
Step 1: Set the equation to zero:
Step 2: Solve for using the quadratic formula:
Here, , , and .
Substitute the values into the quadratic formula:
So, the roots are and .
Step 3: The roots divide the x-axis into intervals: , , and .
Step 4: Test points in each interval to determine the sign of :
For and , choose test points like and .
Both yield negative values for since the parabola opens downwards.
For , test with :
(positive).
Thus, the function is positive for and negative for or .
The correct answer is the interval: or
The function is positive for \( x > 0 : -6 < x < 6
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 \( f\left(x\right) > 0 \).
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