Which of the following is not the graph of a quadratic polynomial?

Options

A.
B.
C.
D.

Explanation

To determine which of the given graphs is not the graph of a quadratic polynomial, we need to understand the characteristics of quadratic polynomials and their graphs.

### Step-by-Step Solution:

1. **Understanding Quadratic Polynomials**:
A quadratic polynomial is generally expressed in the form \( ax^2 + bx + c \), where \( a, b, \) and \( c \) are constants and \( a \neq 0 \). The graph of a quadratic polynomial is a parabola.

**Hint**: Remember that the standard form of a quadratic polynomial is \( ax^2 + bx + c \).

2. **Roots of Quadratic Polynomials**:
A quadratic polynomial can have at most 2 real roots. This means that the graph can intersect the x-axis at either 0, 1, or 2 points.

**Hint**: Consider the maximum number of intersections a parabola can have with the x-axis.

3. **Shape of the Graph**:
The graph of a quadratic polynomial can open upwards or downwards, depending on the sign of the coefficient \( a \):
- If \( a > 0 \), the parabola opens upwards.
- If \( a < 0 \), the parabola opens downwards.

**Hint**: Check the direction of the parabola to determine the sign of \( a \).

4. **Analyzing the Given Graphs**:
- **Graph 1**: This graph touches the x-axis at two points (two equal roots). This is a valid quadratic polynomial.
- **Graph 2**: This graph intersects the x-axis at two distinct points (two distinct roots). This is also a valid quadratic polynomial.
- **Graph 3**: This graph intersects the x-axis at three points. Since a quadratic polynomial cannot have more than 2 real roots, this graph cannot represent a quadratic polynomial.

**Hint**: Count the number of points where each graph intersects the x-axis.

5. **Conclusion**:
Based on the analysis, the graph that intersects the x-axis at three points is not the graph of a quadratic polynomial.

### Final Answer:
The graph that intersects the x-axis at three points is not the graph of a quadratic polynomial.