The graph of the function below does not intersect the -axis.
The parabola's vertex is marked A.
Find all values of where
.
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The graph of the function below does not intersect the -axis.
The parabola's vertex is marked A.
Find all values of where
.
Based on the given graph characteristics, we conclude that the parabola never intersects the -axis and is therefore entirely above it due to opening upwards. This means the function is always positive for every .
Thus, the correct choice is:
Therefore, the solution to the problem is the domain is always positive.
The domain is always positive.
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 \( f\left(x\right) > 0 \).
Look for two key signs: the parabola opens upward (U-shape) and never touches the x-axis. If both are true, then f(x) > 0 for all x values!
It means that no matter what x-value you choose, the function output will always be greater than zero. The parabola stays completely above the x-axis.
The vertex A shows the lowest point of the parabola. Since even this lowest point is above the x-axis, every other point must also be positive. It's not about being greater or less than A!
Parabolas that cross the x-axis have some negative and some positive regions. But this parabola never crosses, so there are no negative regions at all.
Yes! If you have the equation, check the discriminant. When discriminant < 0 and the coefficient of is positive, the parabola never touches the x-axis and stays positive.
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