Is a, which can determine the opening direction of quadratic function, the same as the coefficient a of quadratic term in the general formula of quadratic function?

Is a, which can determine the opening direction of quadratic function, the same as the coefficient a of quadratic term in the general formula of quadratic function?

yes
The vertex formula y = a (X-H) &# 178; + k is the same number as a in the general formula y = ax & # 178; + BX + C