Answer
$(1,2)$
Work Step by Step
The standard form of the given quadratic function, $f(x)=
5x^2-10x+3
,$ is
\begin{array}{l}\require{cancel}
f(x)=\left( 5x^2-10x \right)+3
\\\\
f(x)=5\left( x^2-2x \right)+3
\\\\
f(x)=5\left( x^2-2x+\left( \dfrac{-2}{2} \right)^2 \right)+3-\left( \dfrac{-2}{2} \right)^2
\\\\
f(x)=5\left( x^2-2x+1 \right)+3-1
\\\\
f(x)=5\left( x-1 \right)^2+2
.\end{array}
Since the vertex of $f(x)=a(x-h)^2+k$ is at $(h,k)$, then the vertex of the equation above is
\begin{array}{l}\require{cancel}
(1,2)
.\end{array}
