Answer
If $f\left( x \right)={{\left( x-h \right)}^{2}}+k,$ then $\left( h,\ k \right)$ is the vertex of the parabola.
Work Step by Step
When $f\left( x \right)={{\left( x-h \right)}^{2}}+k,$ where $\left( h,k \right)$ is the vertex of the parabola, this function is called the standard form of a parabola. Parabolas always have a lowest point. This point, where the parabola changes direction, is called the `vertex'. If the quadratic equation is written in the form $y=a{{(x-h)}^{2}}+k,$ then the vertex is the point $\left( h,\ k \right)$.
We are given that the equation $y=5{{x}^{2}}+-20x+15.$
Compare this equation to the standard form of the parabola $y=a{{x}^{2}}+bx+c.$
$a=5\,,\,\,b=-20\,\,,\,c=15$.
x-vertex = $\frac{-b}{2a}=\frac{-\left( -20 \right)}{2\left( 5 \right)}=2$
y-vertex = $5{{\left( 2 \right)}^{2}}-20\left( 2 \right)+15=-5$.
Therefore,
$\begin{align}
& y=5\left( {{x}^{2}}-4x+4 \right)+15-20 \\
& y=5{{\left( x-2 \right)}^{2}}-5\,,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5{{\left( x-2 \right)}^{2}}\ge 0\,. \\
\end{align}$
