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

We know that in points where the curve touches/intersects the 𝑋 − 𝑎𝑥𝑖𝑠 are the zeroes of a polynomial. Therefore, the curve of a quadratic polynomial will touch/intersect the 𝑋 − 𝑎𝑥𝑖𝑠 twice.

In graph (a), the curve does not touch the 𝑋 − 𝑎𝑥𝑖𝑠 at all. This implies that it has no real zeroes. But since the curve can have two imaginary zeroes, graph (a) represents a quadratic polynomial.

In graph (b), the curve touches the 𝑋 − 𝑎𝑥𝑖𝑠 once. This implies that both the zeroes of the polynomial are equal. Thus, graph (b) represents a quadratic polynomial. The curve cannot represent a linear polynomial because its graph is always a straight line.

In graph (c), the curve intersects the 𝑋 − 𝑎𝑥𝑖𝑠 twice. Hence, it has two zeroes. Graph (c) is a quadratic polynomial.

In graph (d), the curve intersects the 𝑋 − 𝑎𝑥𝑖𝑠 at three points. Hence, it represents a cubic polynomial. This implies that graph (d) does not represent a quadratic polynomial.