The expression "8x^2 - 2x + 4" is a quadratic polynomial in the variable x. It consists of three terms: the first term, 8x^2, is a quadratic term, the second term, -2x, is a linear term, and the last term, 4, is a constant. Quadratic polynomials are characterized by their highest degree, which is 2 in this case. To analyze this polynomial, one can find its roots using the quadratic formula or by factoring, if possible. The graph of this polynomial is a parabola that opens upwards, as the coefficient of the quadratic term is positive. The vertex and axis of symmetry can also be determined for further insights into its shape and behavior.