If slope is zero for a quadratic function, the point indicates the maximum value of the function.Select one:TrueFalse

Analysis of the Statement

1. Understanding Quadratic Functions: A quadratic function is generally written in the form $f(x) = ax^2 + bx + c$. For such functions, the slope is represented by the derivative $f'(x) = 2ax + b$.

2. Zero Slope Condition:

   • A zero slope condition ($f'(x) = 0$) indicates that at that point, the function is neither increasing nor decreasing.
   • For a quadratic function, this condition corresponds to either the vertex of the parabola.

3. Nature of the Quadratic:

   • If $a < 0$, the parabola opens downwards, and the vertex represents a maximum point.
   • If $a > 0$, the parabola opens upwards, and the vertex represents a minimum point.

Conclusion

• The statement is True if the quadratic function opens downwards (i.e., $a < 0$), as the vertex would indicate the maximum value.
• Therefore, the statement can be interpreted as true only under the condition that the parabola opens downwards.

Final Answer

True (only for quadratic functions that open downwards).