Graph of a Quadratic Polynomial
Video Explanation
Question
Which of the following is not the graph of a quadratic polynomial?
Solution
Key Property of a Quadratic Polynomial
The graph of a quadratic polynomial
\[ f(x) = ax^2 + bx + c \]
is always a parabola which:
- opens upward or downward
- has exactly one turning point
- never changes direction more than once
Analysis of the Given Graphs
(a) Parabola opening upward → quadratic ✔️
(b) Parabola opening downward → quadratic ✔️
(c) Parabola opening upward → quadratic ✔️
(d) Curve has two turning points → changes direction twice ❌
Such a graph corresponds to a polynomial of degree greater than 2, not a quadratic.
Conclusion
The graph which is not of a quadratic polynomial is:
\[ \boxed{\text{(d)}} \]