If the vertex of a parabola is on the x-axis and the parabola is bending upwards, then the function is always negative except for the vertex point.
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If the vertex of a parabola is on the x-axis and the parabola is bending upwards, then the function is always negative except for the vertex point.
To evaluate the statement about the parabola, we need to understand its properties precisely:
Step 1: Given the parabola's vertex is on the x-axis, we can write its equation in the form , where indicates that it opens upwards.
Step 2: The vertex form of a quadratic function has the vertex with the vertex lying directly on the x-axis. Since , the parabola opens upwards, implying is the minimum point.
Step 3: For points other than the vertex, is always non-negative. Since is positive, . Therefore, the function value at the vertex is zero, and for all other , the function value is positive.
Step 4: Analyze if the function can be negative: With , the value cannot be negative for any value of .
Conclusion: The given statement that the function is "always negative except for the vertex point" is incorrect since outside the vertex, the function is always non-negative and can be positive. Hence, the statement is incorrect.
Therefore, the correct answer 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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