Given
[tex]f(x)=-2x^2+4x-3[/tex]
Solution
[tex]\begin{gathered} f(x)=-2x^2+4x-3 \\ f(x)=ax^2+bx+c \\ in\text{ vertex form} \\ f(x)=a(x-h)^2+k \\ \\ h=-\frac{b}{2a}=-\frac{4}{2(-2)}=-\frac{4}{-4}=1 \\ \\ k=f(h)^ \\ k=-2(1)^2+4(1)-3 \\ k=-2+4-3 \\ k=2-3 \\ k=-1 \end{gathered}[/tex]
The quadratic in vertex form is
[tex]f(x)=-2\left(x-1\right)²-1[/tex]
The vertex is
[tex]Vertex\text{ }\lparen1,-1)[/tex]
Ff
