Answer:
[tex]y=-2(x-1)^2+5[/tex]
Step-by-step explanation:
we have
[tex]y=-2x^2+4x+3[/tex]
This is the equation of a vertical parabola open downward
The vertex represent a maximum
Convert the quadratic equation into vertex form
step 1
Factor -2
[tex]y=-2(x^2-2x)+3[/tex]
step 2
Complete the square
[tex]y=-2(x^2-2x+1)+3+2[/tex]
[tex]y=-2(x^2-2x+1)+5[/tex]
step 3
Rewrite as perfect squares
[tex]y=-2(x-1)^2+5[/tex] ----> equation in vertex form
The vertex is the point (1,5)
