Look at the function below:
Then determine for which values of the following is true:
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Look at the function below:
Then determine for which values of the following is true:
To solve the problem of determining for which values of the quadratic function is less than zero, we should first find the roots of the equation .
Using the quadratic formula, where , , and , we have:
Calculating the discriminant:
Since the discriminant is positive, we will have two distinct real roots:
This gives us:
and
This tells us the quadratic function crosses the x-axis at and .
To determine the sign of the function, consider test values in the intervals determined by the roots, which are: , , and .
Therefore, the solution where is when the variable satisfies or .
Hence, the values of for which are 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 \( f\left(x\right) > 0 \).
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