Análises gráficas e algébricas das repercussões decorrentes da variação dos coeficientes da função quadrática

The objective of this article is to investigate the behavior of a fixed point on the parabola as the coefficients $a, b$ and $c$ of the quadratic function $f(x) = ax2 + bx + c$ vary. The results enhance previous studies for the case of the vertex of the parabola and expand the results to any point, not necessarily the vertex. This in-depth analysis allows for a better understanding of the influence of the coefficients of the quadratic function on the geometry of the curve described by a point that changes as these coefficients vary.