If a parabola is bending upwards and its vertex is below the x-axis, then it is always negative.
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If a parabola is bending upwards and its vertex is below the x-axis, then it is always negative.
The solution to this problem involves understanding the behavior of parabolas. Given that the parabola opens upwards, indicated by , and the vertex is below the x-axis, , here's the detailed explanation:
1. The vertex of the parabola, , is at the lowest point because the parabola opens upwards.
2. With , the value of is negative. However, as moves away from the vertex, the function increases since it opens upwards.
Therefore, for large , becomes positive. For instance, at , the parabola can cross the x-axis and become positive.
Given that the parabola will eventually have positive -values for either very large or very small , the function is not always negative. Hence, the statement that the parabola is always negative is Incorrect.
Incorrect
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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