Answer:
(1,3)
Step-by-step explanation:
The given function is
[tex]y = - 2 {x}^{2} + 4x + 1[/tex]
Factor 2 from the first two terms
[tex]y = - 2( {x}^{2} - 2x) + 1[/tex]
Add and subtract the square of half the coefficient of x.
[tex]y = - 2( {x}^{2} - 2x + 1 - 1) + 1[/tex]
Let us create perfect square trinomial
[tex]y = - 2( {x}^{2} - 2x + 1 ) + - 2 \times - 1 + 1[/tex]
This implies that:
[tex]y = - 2( {x - 1)}^{2}+ 3[/tex]
Therefore the vertex is (1,3).
We got this by comparing to
[tex]y = a( {x - h)}^{2} + k[/tex]
