Question - Analysis of Quadratic Functions

Given the quadratic function \( y = ax^2 + bx + c \), we want to determine if the quadratic \( (P) \) can be formed from the parameters \( a \neq 0 \). This involves calculating the expression \( \frac{b \pm \sqrt{\Delta}}{2a} \), where \( \Delta = b^2 - 4ac \).

To derive the vertex form, we need to ensure that \( \Delta \) is non-negative, leading to real roots that allow for the graphical representation of the quadratic function.