The expression "a_0 + a_1X + a_2X^2" represents a polynomial of degree 2, also known as a quadratic polynomial. In this expression, a_0, a_1, and a_2 are coefficients, which are constants that determine the shape and position of the graph. The variable X is raised to different powers, indicating how the value of the polynomial changes as X varies. Quadratic polynomials are commonly used in various fields, including mathematics, physics, and engineering. They can model a range of real-world phenomena, such as projectile motion and the area of geometric shapes. The graph of a quadratic polynomial is a parabola, which can open upwards or downwards depending on the sign of a_2.