Answer
The quadratic function $f\left( x \right)=a{{\left( x-h \right)}^{2}}+k,a\ne 0$ , is in standard form. The graph of f is called a parabola whose vertex is the point $\left( h,k \right)$. The graph opens upward if a $>0$ and opens downward if a $<0$.”
Work Step by Step
The standard equation of the parabola is given by $f\left( x \right)=a{{\left( x-h \right)}^{2}}+k$.
For the function of the Parabola, the vertex is $\left( h,k \right)$ and the coefficient of ${{x}^{2}}$ decides the opening of the parabola -- either it opens upward or downward.
The condition for opening the parabola is as follow.
If $a>0$ , parabola opens upward and
If $a<0$ , parabola opens downward.
