Aiming at the drawback that the shape of Bézier triangles is fixed with respect to the control points, some blending functions with parameter and with similar properties to the bivariate Bernstein polynomials are presented. Few literatures introduce how do the blending functions are derived. This paper aims at providing the general construction method of adjustable Bézier triangles in polynomial space. With the help of degree elevation technique and based on the idea that the adjustable surfaces are defined by the adjustable control points, the shape adjustable Bézier triangles are defined. The construction process of the blending functions is demonstrated in detail.